UNIVERSITY  OF  CALIFORNIA 
AT   LOS  ANGELES 


GIFT  OF 

CARNEGIE  INSTITU1 
Of   WASHINGTON 


NEW  METHOD 


FOR 


DETERMINING  COMPRESSIBILITY 


THEODORE   WILLIAM   RICHARDS 


WILFRED   NEWSOME   STULL 


WASHINGTON,  U.  S.  A.: 

PUBLISHED   BY   THE   CARNEGIE   INSTITUTION 
December,   1903 


8T4S 


NEW  METHOD 


FOR 


DETERMINING  COMPRESSIBILITY 


THEODORE   WILLIAM   RICHARDS 


WILFRED   NEWSOME   STULL 


WASHINGTON,  U.  S.  A.  : 

PUBLISHED   BY   THE   CARNEGIE   INSTITUTION 
December,   1903 


CARNEGIE   INSTITUTION   OF  WASHINGTON 


PUBLICATION  No.  7 


PlfSSOr 

Til  •»  IIA  Finnic  COMMIT. 
LAICAITt I.  PA. 


IW. 

n/ 


ANNOUNCEMENT. 

This  paper  on  a  "  New  Method  for  Determining  Compressibility  " 
has  been  prepared  by  Professor  Theodore  W.  Richards,  Ph.D.,  Pro- 
fessor of  Chemistry  in  Harvard  University,  and  his  assistant,  Wilfred 
N.  Stull,  S.M.  (Iowa  University),  Edward  Austin  Fellow  of  Harvard 
University.  Its  publication  by  the  Carnegie  Institution  is  recommended 
by  these  chemists  :  Professors  Ira  Remsen,  of  the  Johns  Hopkins  Uni- 
versity ;  F.  W.  Clarke,  of  the  United  States  Geological  Survey,  and 
Edgar  F.  Smith,  of  the  John  Harrison  Laboratory  in  the  University 
of  Pennsylvania. 

This  investigation  was  made  in  the  Chemical  Laboratory  of  Harvard 
College,  Cambridge,  Massachusetts,  and  the  expense  of  it  was  de- 
frayed, in  the  earlier  part,  by  the  Cyrus  M.  Warren  fund  of  Harvard 
University,  and  in  the  latter  part,  by  the  Carnegie  Institution  of  Wash- 
ington. DANIEL  C.  OILMAN, 

President  of  the  Carnegie  Institution. 


209032 


CONTENTS. 

PAGB. 

Introduction 7 

Apparatus 8 

Mercury  and  Glass 17 

Bromine 23 

Iodine 25 

Chloroform  and  Carbon  Tetrachloride 29 

Bromoform 33 

Chlorine 34 

Phosphorus 35 

Water 37 

Heat  of  Compression 39 

New  Manometer  and  Unit  of  Pressure 41 

Table  of  Results 43 

Change  of  Compressibility  with  Pressure 44 

Summary 45 


ILLUSTRATIONS. 

PAGE. 

Fig.  i _ ii 

"       2 12 

"     3 17 

"     4 19 

"     5 32 


NEW  METHOD  FOR  DETERMINING  COMPRESSIBILITY, 

WITH  APPLICATION  TO  BROMINE,  IODINE,  CHLOROFORM,  BROMO- 

FORM,  CARBON  TETRACHLORIDE,  PHOSPHORUS 

AND  WATER. 

BY  THEODORE  WILLIAM  RICHARDS  AND  WILFRED  NEWSOME  STULL. 

INTRODUCTION. 

IT  has  been  suggested  recently  that  since  the  volume  of  a  solid  or 
liquid  must  be  determined  in  part  by  the  internal  pressures  to  which  it 
is  subjected  by  chemical  affinity  and  cohesion,  the  compressibilities  of 
substances  are  probably  data  of  important  chemical  significance.1 

In  attempting  to  interpret  this  significance,  the  enquirer  at  once 
faces  the  fact  that  few  pertinent  compressibilities  are  accurately  known. 
Only  complex  organic  compounds  have  been  much  studied,  and  their 
behavior  under  pressure  is  affected  by  too  many  variables  to  be  easily 
interpreted.  No  more  than  four  elements  have  been  studied  at  all, 
and  none  except  mercury  and  copper  have  been  investigated  by  more 
than  a  single  investigator. 

In  order  to  fill  this  important  gap  in  physicochemical  knowledge,  the 
following  investigation  was  undertaken.  Its  publication  will  be  fol- 
lowed promptly  by  similar  more  extended  publications,  in  which  the 
compressibilities  of  as  many  elements  and  simple  compounds  as  pos- 
sible will  be  treated. 

The  determination  of  compressibility  is  sometimes  considered  as  one 
of  the  most  difficult  of  physical  processes.  The  difficulty  is  due  chiefly 
to  the  fact  that  under  pressure  all  the  parts  of  any  apparatus  change  in 
volume,  and  hence  the  contraction  under  pressure  of  the  substance 
under  examination  is  partly  hidden.  Perhaps  it  is  this  difficulty, 
added  to  a  lack  of  realization  of  the  significance  of  the  data,  which 
has  deterred  investigators  from  undertaking  the  problem  more  syste- 
matically. 

Among  the  various  methods  which  have  been  used,  those  involving 
theoretical  considerations  of  a  mathematical  nature,  such  as  those  com- 
puted from  the  coefficient  of  Poisson,  are  of  somewhat  doubtful  value. 

1Richards,  Proc.  Am.  Acad.  37,  i  (1901),  399  (1902);  38,  293  (1902).  Also 
Zeitschr.  Phys.  Chem.  40:  169,  597;  42:  129  (1902). 

7 


8  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

The  combination  of  stresses  involved  is  not  simple  enough  for  certain 
interpretation. 

The  method  which  attempts  to  correct  itself  by  measuring  the  ex- 
ternal change  in  volume  of  a  bulb  subjected  to  internal  pressure  is 
obviously  faulty,  as  Amagat l  has  pointed  out,  because  the  erroneous 
assumption  is  made  that  the  interior  volume  changes  no  more  than 
does  the  exterior  volume.  Moreover,  such  an  apparatus  can  endure 
but  a  small  pressure,  and  it  is  difficult  to  enclose  it  in  any  other  ap- 
paratus capable  of  withstanding  pressure  without  hiding  the  substance 
under  examination.  Again,  it  is  always  possible  that  this  substance 
may  dissolve  some  of  the  fluid  used  to  transmit  the  pressure,  or  be  dis- 
solved by  it. 

When  a  capillary  glass  tube  is  used  to  contain  a  liquid  under  exam- 
ination, three  serious  errors  are  introduced.  First,  the  bore  and  hence 
the  volume  of  the  tube  increases  under  pressure.  Next,  the  non-con- 
ducting nature  of  the  walls  prevents  the  compression  from  being 
strictly  isothermal,  while  the  heat  capacity  of  the  walls  prevents  it 
from  being  strictly  adiabatic.  From  the  work  of  Barus,2  who  has 
carried  out  the  most  successful  and  comprehensive  experiments  accord- 
ing to  this  method,  it  may  be  inferred  that  these  errors  in  some  cases 
nearly  counterbalance  one  another.  Another  cause  of  error  is  the 
adhesion  of  the  compressed  liquid  to  the  emptied  tube,  as  the  column 
shortens  under  pressure,  a  circumstance  which  causes  the  compression 
to  appear  too  large.  Moreover,  the  compressibility  of  liquids  is  so 
slight  that  very  small  changes  in  length  of  column  must  be  accurately 
observed,  when  the  liquid  is  arranged  in  a  uniform  thread.  The  most 
serious  causes  of  error  having  been  reviewed,  it  is  possible  to  describe 
the  forms  of  apparatus  which  we  have  used  in  order  to  avoid  them. 

APPARATUS. 

In  order  to  obviate  the  uncertainty  of  temperature,  and  the  last 
mentioned  difficulty  of  measurement,  we  decided  to  enclose  the  greater 
part  of  the  liquid  to  be  examined  in  a  thin  glass  bulb.  Barus,  indeed, 
had  seen  the  advantage  of  this  arrangement,  but  he  was  unable  to  pre- 
vent the  fracture  of  the  bulb  under  comparatively  small  pressures.  In 
order  to  obviate  this  difficulty,  we  surrounded  the  bulb  with  mercury, 
and  subjected  the  exterior  to  the  same  pressure  as  that  applied  to  the 
liquid  within.  The  balancing  of  pressure  prevented  the  bulb  from 
bursting,  and  the  great  thermal  conductivity  of  mercury  soon  estab- 

1  Amagat,  Am.  Chem.  Phys.  (6),  82,  95  (1891). 
•Bull.  U.  S.  Geolog.  Survey,  No.  92  (1892). 


APPARATUS  9 

lished  constancy  of  temperature.  The  change  of  volume  could  be 
sharply  read  in  a  connecting  capillary  tube. 

In  order  to  determine  the  changes  of  volume  suffered  by  this  bulb 
and  tube  under  various  pressures,  we  used  mercury  as  a  standard  sub- 
stance, depending  upon  the  very  satisfactory  results  of  Amagat '  for 
our  knowledge  of  its  absolute  compressibility.  The  results  are  care- 
fully stated  below  in  such  a  way  that  if  any  error  is  discovered  in  the 
compressibility  of  this  standard  substance,  the  more  accurate  value  may 
be  easily  applied.  It  will  be  seen  that  when  the  absolute  compressi- 
bility of  a  single  substance  is  once  accurately  known,  the  reference  of 
all  other  substances  to  it  becomes  a  very  simple  matter.  It  is  to  be 
hoped,  therefore,  that  many  investigators  will  determine  by  many 
methods  the  absolute  compressibility  of  mercury,  a  substance  which 
for  several  reasons  forms  an  exceedingly  convenient  standard.  We 
propose  ourselves  to  do  this  in  the  future ;  but  for  the  purpose  of  this 
paper  the  value  of  Amagat  is  quite  certain  enough. 

The  apparatus  thus  constituted  demands  a  stout  envelope  around 
each  end  of  the  bulb  tube,  with  a  free  space  of  capillary  tube  between. 
The  lower  of  these  two  envelopes  consisted  of  the  compressing  barrel 
of  the  admirable  Cailletet  machine  made  by  the  Societe"  Genevoise  for 
liquefying  small  amounts  of  gas.  In  our  arrangement  the  free  space 
of  capillary  tube  was  visible  through  an  oval  opening  or  window  in 
the  brass  support  which  carried  the  upper  envelope.  This  upper 
envelope  in  turn  was  closed  by  a  heavy  steel  screw  cap  with  an 
attached  tube  for  transmitting  the  pressure.  The  capillary  was 
cemented  into  each  envelope  by  means  of  marine  glue,  and  was  cali- 
brated with  suitable  care. 

Because  the  use  of  this  apparatus  was  subsequently  abandoned, 
further  description  of  it  is  unnecessary.  We  are  indebted  to  Mr. 
Frederic  Bonnet,  Jr.,  for  assistance  in  this  part  of  the  work. 

While  the  device  overcomes  the  difficulties  which  it  was  expected  to 
overcome,  three  other  causes  of  trouble  still  remained.  These  are, 
the  mutual  solubility  of  the  liquids  at  the  point  of  contact  in  the  capil- 
lary tube,  the  adhesion  of  the  compressed  liquid  to  the  wall  of  this 
tube  from  which  it  has  retreated,  and  the  frequent  fracture  of  the  free 
portion  of  the  tube  at  pressures  of  even  less  than  four  hundred  atmo- 
spheres. 

In  our  first  experiments  with  bromine,  we  used  water  saturated 
with  this  substance  as  the  containing  or  compressing  liquid ;  but  we 

1  Loc.  cit.  The  value  found  by  Amagat  is  0.000003  92  '*  the  unit  of  pressure  is 
the  atmosphere,  or  0.000003  8°  if  the  unit  is  the  kilogram  per  sq.  cm. 


10  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

had  no  knowledge  of  the  change  of  solubility  of  bromine  in  water 
with  change  of  pressure.  Moreover,  the  bromine  in  the  vicinity  of 
water  must  have  been  saturated  with  the  latter  substance ;  hence 
the  result  was  at  best  an  approximation.  When  the  bulb  was  in  the 
upper  receptacle,  the  force  of  gravity  assisted  the  adhesion  of  the  bro- 
mine to  the  walls  of  the  tube,  and  the  adhering  bromine  was  clearly 
visible ;  but  when  the  bulb  was  below,  gravity  had  the  contrary  effect, 
and  the  adhesion  became  less  serious. 

In  the  first  position,  a  pressure  of  50  kilograms  per  square  centi- 
meter was  found  in  one  tube  to  cause  an  apparent  compression  of 
0.284  Per  cent-  °f  tne  volume  of  the  bromine  and  0.007  Per  cent-  °f  tne 
volume  of  the  mercury.  Thus  the  difference  between  the  compressi- 
bility of  mercury  and  bromine  was  found  to  be  0.000055  4?  *ne  uru°t  °f 
pressure  being  taken  as  a  kilogram  per  square  centimeter.  Adding  to 
this  the  compressibility  of  mercury,  0.00000380,  the  value  0.000059  2 
is  obtained  for  that  of  bromine,  a  value  probablv  too  high  for  the 
reasons  already  named. 

Other  trials,  with  a  wider  tube  and  with  the  bulb  in  the  lower  envel- 
ope, diminished  the  error  due  to  the  adhesion  of  bromine.  Thus  the 
percentage  change  of  volume  for  pressures  of  50,  100,  and  150  kilo- 
grams per  square  centimeter  respectively  were  found  to  be  0.272, 
0.538  and  0.797  per  cent,  for  bromine,  and  0.011,0.022  and  0.033 
per  cent,  for  mercury  respectively.  These  data  lead  to  the  following 
values  of  the  compressibility  of  bromine  —  from  o  to  50  atmospheres, 
0.0000582  ;  from  50  to  100  atmospheres,  0.0000576  ;  and  from  100  to 
150  atmospheres,  0.0000570.  The  temperature  was  17°  C.  As  will 
be  seen  later,  these  values  are  not  far  from  the  true  ones ;  and  they  are 
consistent  enough  to  show  a  steady  decrease  of  compi'essibility  with 
increasing  pressure,  which  seems  to  be  the  universal  rule. 

The  experience  thus  gained  led  to  the  devising  of  a  new  method  re- 
taining all  the  advantages,  and  at  the  same  time  obviating  all  the  dis- 
advantages of  the  previous  procedure.  In  this  new  method,  the  bro- 
mine, instead  of  being  in  contact  with  any  other  fluid,  was  enclosed 
hermetically  in  a  very  thin,  flat  flexible  glass  bulb,  containing  no  other 
substance.  The  decrease  of  volume  in  this  bulb  upon  compression  was 
determined  as  if  it  were  a  homogeneous  solid,  by  compressing  it 
under  mercury  in  a  suitable  vessel  to  be  described  later.  Allowance 
is  easily  made  for  the  change  in  volume  of  the  mercury  and  glass,  if 
the  containing  apparatus  has  been  properly  tested  full  of  mercury  in 
the  first  place. 

Since  the  bulbs  were  so  thin  as  to  collapse  under  a  pressure  of  less 


APPARATUS 


than  the  quarter  of  an  atmosphere,  the  pressure  within  them  must 
have  been  essentially  the  same  as  that  applied  without.  Some  ex- 
perience and  art  were  needed  in  order  to  prevent  these  bulbs  from 
being  so  thin  in  places  as  to  be  fractured  by  the  buoyant  pressure  of  the 
mercury;  and  a  number  of  exasperating  accidents  oc- 
curred from  this  cause.  It  is  perfectly  possible,  however,  ji ,  !; 
to  make  a  glass  bulb,  containing  several  cubic  centimeters, 
which  will  change  under  pressure  by  five  per  cent,  of  its 
volume  and  yet  be  strong  enough  to  endure  immersion  in 
mercury.  Our  experiments  were  made  with  such  bulbs. 
The  diagram  (Fig.  i )  represents  one  of  them.  Their  flat- 
tened sides  were  best  produced  by  well  directed  heating 
after  the  cylindrical  shape  had  been  first  attained. 

For  the  purpose  of  filling,  the  neck  of  the  bulb  was  at 
first  drawn  down  stoutly  in  the  fashion  indicated  by  the 
dotted  lines  in  Fig.  i .  After  having  been  filled  by  means 
of  a  capillary  funnel  tube,  the  bulb  was  packed  in  ice  and 
water.  When  the  liquid  within  had  contracted  so  much  as 
to  leave  the  narrowed  part  far  above  the  meniscus,  this 
narrow  portion  was  drawn  out  to  a  very  fine  point,  the  bulb 
itself  being  shielded  from  the  heat  by  asbestos.  Upon 
warming  the  bulb  through  a  degree  or  two  this  capillary 
point  was  at  once  filled  with  liquid,  and  was  then  sealed  by  fusion, 
usually  without  enclosing  a  visible  trace  of  air,  and  always  without 
enclosing  a  measurable  trace.  The  weight  of  the  glass  in  the  bulb 
was  always  determined,  either  by  subtracting  the  drawn-off  tip  from 
the  total  original  weight,  or  else  by  weighing  the  glass  fragments  after 
the  experiment.  The  weight  of  the  enclosed  liquid  was  obtained  by 
weighing  the  sealed  bulb,  and  subtracting  from  this  the  weight  of  the 
glass. 

The  bulb  having  been  filled  at  two  or  three  degrees  above  zero  the 
expansion  of  the  liquid  within  caused  the  walls  of  the  vessel  to  swell 
outward  at  20°  ;  and  thus  the  possibility  of  compression  of  the  bulb  at 
ordinary  temperatures  was  greatly  increased.  In  the  calculations  the 
slight  compressibility  of  the  glass  of  this  bulb  was  taken  into  account. 

It  is  now  necessary  to  describe  the  apparatus  containing  mercury  by 
means  of  which  the  decrease  in  volume  of  the  bulb  was  found.  This 
apparatus,  pictured  in  Fig.  2,  consisted  simply  of  a  wide  short  test 
tube,  with  a  very  well  ground  hollow  stopper  terminating  above  in 
a  fine  funnel  tube  provided  with  a  downward  pointing  platinum  wire. 
For  the  sake  of  clearness  this  apparatus  will  always  be  called  the  glass 


FIG. 


12 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


jacket.  It  was  filled  with  the  liquid  metal,  and  the  change  in  volume 
for  different  pressures  was  measured  very  simply  by  placing  the  whole 
jacket  under  the  liquid  in  the  Cailletet  barrel,  adding  successive  weighed 
portions  of  mercury,  and  noting  each  time  the  pressure 
needed  just  to  break  and  then  again  make  the  electrical 
connection  between  the  meniscus  and  the  platinum 
point.  The  electrical  method  of  indication  has  often 
been  used  for  similar  purposes,  especially  by  Barus  and 
Amagat ;  but  never  in  exactly  this  way.  If  the  plati- 
num wire  is  very  finely  pointed,  the  fine  tube  around  it 
about  1.5  mm.  in  diameter  and  the  meniscus  perfectly 
clean,  the  indications  of  this  instrument  are  surpris- 
ingly constant  and  trustworthy.  Even  with  a  substance 
no  more  compressible  than  mercury  it  is  easy  to  be 
certain  of  the  necessary  pressure  within  one  atmos- 
phere— a  very  small  fractional  error  in  many  hundred 
atmospheres.  The  pressure  at  which  the  connection 
was  made  was  taken  as  the  true  point,  rather  than  that 
at  which  the  connection  was  broken,  since  there  is 
sometimes  a  slight  adhesion  between  the  point  and  the 
mercury  under  the  last  named  circumstances.  Often, 
however,  the  making  and  breaking  occurred  within  an 
atmosphere's  pressure  of  one  another. 

If  the  fine  tube  is  larger  than  1.5  mm.,  the  sensibility 
of  the  instrument  is  reduced ;  if  it  is  much  less  than 
1.5  mm.,  drops  of  mercury  are  likely  to  be  caught  and 
held  by  the  wire. 

The  most  serious  possible  cause  of  error  arises,  how- 
ever, from  the  faulty  fitting  of  the  ground  stopper  of 
the  glass  jacket.  If  a  poorly  ground  stopper  be  used, 
the  mercury  during  the  process  of  compression  is  forced 
into  the  tiny  interstices  between  stopper  and  tube  —  a 
complication  which  makes  the  compressibility  of  the 
liquid  seem  slightly  greater  than  it  is.  This  difficulty 
may  be  obviated  wholly  by  always  wetting  the  ground 
surfaces  with  a  minute  drop  of  water  or  some  other 
liquid,  thus  displacing  all  the  air,  and  preventing  the 
ingress  of  mercury.  The  infinitesimal  variations  in  the  compression 
of  this  practically  constant  drop  of  lubricating  liquid  are  quite  too 
small  to  produce  any  perceptible  effect,  and  successive  trials  always 
yield  the  same  result. 


FIG.  2. 


APPARATUS 


The  filling  of  the  simple  apparatus  was  conducted  in  the  following 
manner.  The  lower  tube  of  the  glass  jacket  was  filled  with  mercury, 
a  single  drop  of  water  was  placed  on  its  surface,  and  the  stopper  was 
carefully  inserted  and  tied  down  with  stout  string  passed  over  a  rubber 
shoulder.  The  latter,  used  to  give  needed  elasticity,  is  indicated  by 
dotted  lines  in  Fig.  3.  The  cavity  in  the  stopper  was  filled  with 
mercury  from  above  by  means  of  a  capillary  funnel  tube,  as  far  as  the 
point  of  the  platinum  wire ;  and  the  mercury  surface  was  separated 
from  the  mineral  oil  of  the  Cailletet  compression  barrel  by  water, 
which  filled  the  upper  part  of  the  funnel  tube.  As  already  stated  the 
meniscus  must  be  perfectly  clear  and  free  from  oil,  otherwise  its  curve 
is  irregular.  In  order  to  conduct  away  the  heat  of  compression  and  to 
make  the  lower  electrical  contact,  mercury  was  poured  around  the 
outside  of  the  lower  two  thirds  of  the  glass  jacket. 

The  upper  platinum  wire  was  connected  with  an  insulated  wire 
running  through  a  capillary  glass  tube  sealed  into  the  upper  movable 
part  of  the  Cailletet  apparatus,  and  the  contact  was  detected  with  the 
help  of  a  feeble  cell  and  a  delicate  index-galvanometer.  The  appara- 
tus being  tightly  screwed  into  place,  pressure  was  applied  until  the 
circuit  was  broken  —  a  condition  which  showed  that  the  mercury  had 
been^  compressed  until  its  meniscus  had  fallen  below  the  platinum 
point.  The  mercury  was  kept  at  this  point  for  twenty  minutes,  or 
until  the  pressure  readings  became  constant.  The  heating  effect  of  the 
compression  was  considerable ;  but  the  inner  jacket  being  immersed  in 
mercury,  the  heat  was  quickly  conducted  away  to  the  large  surround- 
ing thermostat,  kept  constant  to  within  0.01°  C.,  in  which  the  Cailletet 
barrel  was  immersed.  An  idea  of  the  speed  of  this  equalization  of 
temperature  can  be  gained  from  the  following  table.  Here  the  pres- 
sures corresponding  to  the  break  of  electrical  contact  are  given  at 
various  times,  beginning  with  the  time  of  the  first  quick  compression : 


Tim< 

:. 

Pressure  at  which  Contact  was  Broken, 
kg./cm*. 

O  S( 

C. 

410 

2O 

352 

40 

345 

i  m 

n- 

340 

2 

335 

3 

331 

4 

327 

5 

326 

10 

326 

15 

326 

20 

326 

14  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

Constancy  in  the  readings  was  reached  in  five  minutes.  The  glass 
jacket  in  this  case  contained  a  bulb  of  chloroform  immersed  in  the 
mercury. 

The  quantity  of  mercury  in  the  glass  jacket  was  usually  so  adjusted 
that  the  first  constant  pressure  reading  was  between  fifty  and  one  hun- 
dred atmospheres,  and  this  first  reading  was  taken  as  the  starting  point 
of  the  determination.  Minute  air  bubbles  were  thus  disarmed  of  pos- 
sible injurious  effect.  As  already  suggested,  a  weighed  quantity  of 
mercury  was  now  added  through  the  funnel  tube  (see  Fig.  2)  and 
pressure  again  applied.  The  added  pressure  necessary  to  break  the 
electrical  circuit  corresponded  to  the  volume  of  the  extra  mercury  in- 
troduced. This  process  was  repeated  until  the  highest  pressure  was 
reached,  and  thus  were  found  the  points  on  a  curve  which  depicts  the 
difference  between  the  compressibilities  of  mercury  and  glass.  Only 
in  the  most  accurate  work  is  it  necessary  to  consider  the  compression 
of  the  small  extra  volumes  of  mercury  introduced,  since  the  omission 
of  this  correction  causes  an  error  of  only  0.04  of  one  per  cent,  for  every 
hundred  atmospheres. 

If  now  there  is  introduced  beneath  the  mercury  the  substance  whose 
compressibility  is  to  be  determined,  and  a  new  curve  is  found  in  the 
same  way,  it  is  evident  that  the  differences  between  these  two  curves 
represent  the  differences  between  the  compressibility  of  the  new  sub- 
stance and  an  equal  volume  of  mercury. 

A  typical  series  may  better  serve  to  make  clear  the  method  of  obser- 
vation and  calculation.  The  first  process  is  the  calibration  of  the  glass 
jacket  with  mercury  already  described.  The  pressure  readings  given 
below  were  taken  after  successive  additions  of  mercury,  the  whole 
apparatus  being  filled  with  this  liquid. 

Initial  reading:  Circuit  made  37,  37,  37,  37,  37  kg. /cm2.  Circuit 
broken,  40,  39,  39,  39,  39  kg/cm2. 

After  adding  first  quantity  of  mercury,  =0.1020  gram.  Circuit 
made  254,  255,  254,  254,  254  kg./cm*.  Circuit  broken  257,  256, 
256,  256,  256  kg./cm1. 

After  adding  second  quantity  of  mercury,  =  0.0998  gram.  Circuit 
made  476,  476,  476,  476  kg./cm*.  Circuit  broken  478,  478,  478, 
478  kg./cm'. 

After  adding  third  quantity  of  mercury,  =  0.0660  gram.  Circuit 
made  632,  634,  634,  634,  634  kg./cm*.  Circuit  broken  636,  636,  636, 
636,  636  kg./cm2. 

A  bulb  filled  with  bromine  was  now  put  into  the  jacket ;  the  remain- 
ing space  was  filled  with  mercury  and  a  new  series  of  pressure 


APPARATUS  I  5 

readings  taken.  The  weight  of  the  bromine  was  7.502  grams,  while 
the  thin  containing  bulb  weighed  only  0.72  gram. 

Initial  reading:  Circuit  made  68,  68,  68,  68,  68  kg./cm'''.  Circuit 
broken  70,  70,  70,  71,  69  kg.  /cm2. 

After  adding  first  quantity  of  mercury,  =±  0.3338  gram.  Circuit 
made  223,  223,  223,  223  kg.  /cm2.  Circuit  broken  227,  225,  225,  225 
kg.  /cm2. 

After  adding  second  quantity  of  mercury,  =0.3357  gram.  Circuit 
made  391,  392,  392,  392,  392  kg./cm2.  Circuit  broken  393,  394, 
393>  393  kg./cm2. 

After  adding  third  quantity  of  mercury,  =  0.3259  gram.  Circuit 
made  566,  565,  565,  565,  565,  565  kg./cm2.  Circuit  broken  567, 
567>  569>  567»  568>  567  kg./cm2. 

From  the  results  with  mercury  a  curve  is  plotted  with  pressures  as 
abscissas  and  total  weights  of  mercury  as  ordinates.  The  ordinates  on 
this  curve  which  correspond  to  the  pressures  found  in  the  series  with 
bromine  evidently  represent  the  weights  of  mercury  which  are  to  be 
subtracted  from  the  weights  actually  added  in  the  bromine  series  in 
order  to  obtain  a  basis  for  calculating  the  difference  between  the 
volume  change  of  the  bromine  and  the  change  in  an  equal  volume  of 
mercury. 

The  equation  for  calculating  the  average  compressibility  between 
the  pressures  Pl  and  P^  i.  e.,  the  volume  change  for  a  unit  of  the 
original  volume  subjected  to  an  increase  of  a  unit  of  pressure,  is 
obviously  : 


W(Pl  - 
where 


£,  /9',  and  /3"  equal  respectively  the  average  compressibilities  of  the 

substance  studied,  mercury,  and  glass  ; 
TV  and  TV'  equal  respectively  the  two  weights  of  mercury  in  the  two 

series  above    described    corresponding   to   the   given  change   of 

pressure  Pl  —  Pt. 
TV"  and  Pf  respectively  the  weights  of  the  thin  glass  bulb  and  the 

substance  studied  ; 

d  and  D  the  densities  of  glass  and  of  this  substance,  and, 
13.546  the  density  of  mercury  at  20°. 
The  value  £'  —  /?"  is  obtained,  as  will  be  seen  later,  directly  in  the 


1  6  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

first  or  mercury  series  by  dividing  the  added  weight  of  mercury  by  the 
product  of  the  total  weight  of  mercury  and  the  added  pressure. 


For  the  absolute  value  of  /9'  ;  we  have  had  to  depend  upon  Amagat's 
work,  as  already  stated  —  an  investigation  that  gives  this  value  only  as 
far  as  fifty  atmospheres.  Since  the  magnitude  of  /9'  is  never  greater 
than  0.00000380,  a  slight  variation  in  it  with  the  pressure  can  be  of 
no  serious  importance  in  the  present  work.  In  order,  however,  to 
make  as  easy  as  possible  the  correction  of  our  results  in  case  our  as- 
sumed value  of  /?'  is  in  error,  there  is  recorded  below  not  only  the 
value  J3,  but  also  the  value  /9  —  ft'  '  .  This  quantity  /?  —  /$'  relies  essen- 
tially upon  our  own  work,  and  at  any  time  the  compressibility  /9  may 
be  found  from  it  by  adding  the  most  probable  compressibility  of 
mercury. 

The  same  apparatus  serves  for  determining  the  compressibility  of 
solids  ;  but  with  liquids  which  do  not  attack  mercury  a  still  simpler 
device  may  be  used.  The  thin  walled  bulb  may  be  dispensed  with, 
and  the  jacket  itself  used  to  contain  the  liquid.  In  this  case  a  doubly 
bent  tube  must  be  attached  above,  in  order  to  contain  the  mercury 
necessary  for  making  electrical  contact.  The  apparatus  thus  assumes 
the  form  shown  in  Fig.  3,  the  stopcocks  being  affixed  to  facilitate  fill- 
ing. For  the  most  accurate  work  it  would  be  better  to  omit  these 
stopcocks,  and  to  fill  the  jacket  by  exhausting  the  air  ;  because  the 
stopcocks  are  liable  to  leak  unless  very  well  ground,  and  their  presence 
introduces  a  slight  uncertainty  due  to  the  small  amount  of  liquid  con- 
tained in  their  channels.  In  our  experiments  this  small  volume, 
amounting  to  only  0.002  of  the  whole,  could  be  safely  neglected. 
It  is  well  not  to  heat  the  glass  to  a  high  temperature,  during  the 
filling,  because  of  its  well-known  volume  lag.  On  the  other  hand, 
we  have  as  yet  been  unable  to  detect  any  appreciable  volume  lag 
on  compression.  This  is  shown  by  the  fact  that  series  of  experiments 
made  by  taking-  out  mercury  after  the  attainment  of  high  pressure  give 
results  identical  with  those  obtained  by  gradually  adding-  mercury. 

After  being  thoroughly  cleaned  this  jacket  was  filled  with  mercury 
and  the  stopcocks  were  closed.  The  mercury  was  arranged  at  a  level 
slightly  above  the  lower  point  of  the  upper  wire  and  the  funnel  tube 
above  was  filled  with  pure  water  as  before. 

The  jacket  was  placed  in  the  Cailletet  barrel,  and  the  pressures 
corresponding  to  successive  added  portions  of  mercury  were  found  in 
the  way  already  described.  Thus  the  mercury  curve  was  determined. 


APPARATUS 


The  greater  part  of  the  mercury  was  now  withdrawn,  and 
due,  filling  the  U-tube  at  least,  was  weighed  with  the  glass, 
quently  the  liquid  under  investigation  was  drawn 
in,  completely  displacing  the  air ;  and  finally  the 
apparatus,  after  external  drying,  was  weighed 
again.  Thus  was  found  the  weight  of  the  liquid 
to  be  compressed. 

The  jacket  was  now  placed  once  more  in  the 
Cailletet  barrel,  and  once  more  the  pressures  cor- 
responding to  successive  added  portions  of  mercury 
were  found.  These  new  readings  define  the  curve 
of  compressibility  of  the  liquid  and  the  residual 
mercury.  The  differences  between  the  weights  of 
mercury  added,  for  any  given  change  of  pressure, 
as  found  on  the  two  curves,  give  by  simple  calcu- 
lation the  differences  between  the  compression  of 
the  given  volume  of  liquid  and  the  same  volume 
of  mercury,  hence  the  compressibility  is  easily 
computed  with  the  help  of  the  following  equation, 
in  which  the  symbols  have  the  same  significance 
as  before. 


the  resi- 
Subse- 


13 


COMPRESSIBILITY  OF  MERCURY  AND  GLASS. 

Since  both  the  difference  between  the  compres- 
sibility of  glass  and  mercury  and  the  absolute  com- 
pressibility of  mercury  enter  into  the  equations, 
it  is  important  at  the  outset  to  determine  these 
quantities  as  definitely  as  possible.  Accordingly 
several  careful  series  of  experiments  were  made. 
Because  the  change  in  the  capacity  of  a  hollow 
glass  vessel  under  compression  is  equal  to  the 
change  in  the  same  volume  of  solid  glass,  the  value 
/9'  —  /3"  may  be  determined  by  compressing  mer- 
cury in  the  jacket  already  described.  Three  of 
these  jackets,  numbered  I,  II  and  III,  were  of  the 
type  suitable  for  solids  depicted  in  Fig.  2,  while 
the  fourth  was  of  the  type  designed  for  liquids, 
depicted  in  Fig.  3.  In  the  table  below  the  actual 
figures  found  with  these  four  jackets  are  given,  and  in  the  third 
column  the  added  weights  of  mercury  TV'  are  all  divided  by  the  total 


FIG.  3. 


i8 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


weight  of  mercury  W  in  order  to  reduce  all  the  results  to  a  compar- 
able basis,  namely,  the  results  which  would  have  been  obtained  if  the 
jackets  had  each  held  only  a  gram  of  the  metal.  The  fourth  column 
contains  this  quantity  with  an  added  quantity  an  constant  with  each 
series.  This  an  is  necessary  to  reduce  these  measurements  beginning 
at  various  pressures  to  the  same  starting  point.  The  method  of  doing 
this  is  explained  in  the  following  paragraph. 

COMPRESSION  OF  MERCURY  IN  GLASS. 


Number  of 
Jacket. 

Total  Weight 
of  Mercury 
at  20°  C. 

w>  =  Weight 
of  Added 
Mercury. 

a/' 

W' 

£+«. 

Pressure  Cor- 
responding. 

I. 

grams. 
328 

milligrams. 
0 
102.0 
201.8 
267.8 

milligrams. 
O 
0.3II 
0.615 
O.8I4 

milligrams. 
0.055  =  ai 

kg.  /cm2. 

37 

254 

476 

634 

II. 

437 

O 

153-2 
273.2 

0 

Q-351 
0.623 

0.  143  =  flu 
0-494 
0.765 

98 

347 
547 

III. 

308.6 

0 

106.6 
166.9 

o 
0-345 
0.541 

o.  176  =  dm 
0.521 
0.717 

I22.O 

IV. 

291.6 

0 

118.9 

0 

0.407 

0.523 

80 
365 

The  results  are  best  compared  by  graphic  method,  hence  a  diagram 
is  given  herewith  (Fig.  4).  The  portion  of  the  curve  below  37  atmos- 
pheres is  extrapolated  (a  proceeding  which  is  indicated  by  the  dotted 
line)  and  the  second,  third  and  fourth  series  are  begun  intentionally  on 
the  curve  of  the  first.  an  is  in  each  case  the  ordinate  corresponding  to 
the  first  pressure  of  each  series.  Hence  the  lowest  four  points  are 
fixed  arbitrarily  and  the  agreement  of  the  results  is  shown  only  by  the 
seven  points  at  the  pressures  above  200  atmospheres.  This  agreement 
is  nevertheless  close  enough  to  satisfy  the  most  exacting  requirements  of 
the  present  work.  The  third  series  of  experiments  was  made  by  Mr. 
Frederick  Bonnet,  Jr. 

This  curve  represents  various  values  of  ft'  —  /9",  or  the  differences 
between  the  compressibilities  of  glass  and  mercury  at  different  pres- 
sures, both  being  at  20°.  After  having  been  plotted  several  times  on 
a  large  scale,  the  most  probable  values  for  this  quantity  were  found 
from  the  averages  to  be  those  recorded  on  page  20. 

Thus  there  is  a  steady  decrease  in  the  value  of  (/3'  —  p")  as  the  pres- 
sure decreases.  Without  further  data  it  is  impossible  to  determine  how 
much  of  this  decrease  is  due  to  the  glass  and  how  much  to  mercury ; 


MERCURY    AND    GLASS 


.but  fortunately  Amagat's  results  enable  us  to  decide.  He  found  by 
measuring  linear  compression  that  glass  possessing  below  500  atmo- 
spheres an  average  compressibility  of  0.00000225  decreased  in  com- 


X  / 


PRESSURE    100 


300  400 

FIG.  4. 


pressibility  only  a  unit  in  the  last  decimal  place  between  500  and  i  ,000 
atmospheres.  Hence  the  compressibility  of  glass  is  almost  a  constant, 
and  its  curve  with  increasing  pressure  practically  a  straight  line. 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


Range  of  Pressure. 

(?'  —  (3")  10". 

Probable  Values  of  Compressi- 
bility of  Mercury.     (See 
Explanation  Below.) 

kg./cm». 

U'.do"). 

O-IOO 

I.48 

3.80 

I  OO-2OO 

1-43 

3-75 

200-300 

1.40 

3-72 

300-400 

1-37 

3-69 

400-500 

1.32 

1.64 

500-600 

1.28 

3.60 

Therefore  the  progressive  change  in  the  value  ft'  —  ft"  given  above 
must  be  due  to  the  mercury  alone,  if  the  pressure  readings  were  exact. 

The  quantity  /3",  while  constant  for  any  one  kind  of  glass  varies 
considerably  with  different  kinds  of  glass.  Amagat  found  values 
ranging  from  0.0000022  to  0.0000025. 

In  our  case  the  constant  ft"  is  easily  found  by  subtracting  the  first 
value  of  ft'  —  ft"  from  the  compressibility  of  mercury  3.80  x  lO"8  found 
by  Amagat.  ft"  =  ft'  —  (ft'  —  ft")  =  (3.80  —  1.48)  io~8  =  2.32  -  io~«. 
This  result  corresponds  well  with  Amagat's. 

It  is  possible  now  to  obtain  a  close  approximation  to  the  values  of 
ft*  for  pure  mercury  by  adding  the  constant  ft"  to  the  values  ft'  —  ft", 

The  values  given  in  the  last  column  of  the  table  are  computed  in 
this  way.  They  are  not  certainly  exact,  but  will  amply  serve  the  pur- 
pose of  this  paper. 

Unfortunately  Amagat  does  not  state  the  temperature  at  which  his 
value  for  mercury  0.00000318  was  found.  Accordingly,  by  comparing 
the  behavior  of  a  jacket  filled  with  mercury  at  o°  with  one  at  20°,  we 
sought  to  trace  the  possible  magnitude  of  the  uncertainty. 

A  change  in  pressure  from  155  to  563  kilogi-ams  per  square  centi- 
meter required  an  additional  weight  of  mercury  of  0.2486  gram  or 
0.01830  milliliter  at  o°,  while  the  same  change  in  pressure  required 
0.2475  gram  or  0.01828  milliliter  at  20°.  These  two  volumes  are 
almost  exactly  identical,  hence  ft'  —  ft"  does  not  change  sensibly  with 
the  temperature.  In  other  words,  the  compressibility  of  glass  and 
mercury  change  by  the  same  actual  amount  in  20°.  But  Amagat 
found  that  the  compressibility  of  glass  changes  about  3  per  cent,  for 
100°  C. —  or  about  0.000000014  f°r  2O°-  Hence  if  the  compressi- 
bility of  mercury  at  20°  is  0.00000380,  the  compressibility  at  o°  must 
be  0.000003786.  This  difference  of  one  third  of  one  per  cent,  is  too 
small  to  produce  any  essential  effect  on  our  work,  causing  for  example 
only  an  uncertainty  of  one  fiftieth  of  one  per  cent,  in  the  compressi- 
bility of  bromine. 


MERCURY    AND    GLASS  21 

While  the  value  of  ft'  —  ft"  varies  perhaps  from  i  .48  x  io~*  to 
1.28  x  io~*  in  a  range  of  600  atmospheres,  it  is  nevertheless  sufficiently 
constant  to  make  possible  a  simplification  of  equation  (i)  on  page 
15  without  the  introduction  of  appreciable  error.  Noting  that 
£'  =  0.0000038,  ft'  —  ft"  =  0.0000014  and  d  =*  the  density  of  glass 
=  2.5  we  have 

ft.     Jy 


"3-55 

0.000  001  4W"  QPj 


.U    y  /> 

J        (^-)' 


Since  both  /S'/^  and  the  second  term  within  the  parentheses  are  very 
small,  the  value  (i  —  ft  P^)  may  be  removed  outside  of  the  parentheses 
without  introducing  appreciable  error.1  The  equation  thus  becomes  : 


+  0.0000076  „'</>,  -/>)]  -.         (5) 

This  equation  was  used  in  calculating  all  the  results.  When  the 
inner  thin  glass  bulb  was  omitted,  in  the  case  of  liquids  not  attacking 
mercury,  w"  becomes  zero  and  the  third  term  within  the  first  paren- 
theses drops  out.  The  equation  then  assumes  the  form  of  equation 
(3)  on  page  17. 

The  value  of  TV'  used  in  the  equation  above  must  of  course  corre- 
spond to  the  same  range  of  pressure  (Pl  —  />,)  as  that  observed  in  the 
case  of  TV.  The  value  is  easily  found  from  equation  (2). 

iu>  =  W'P^  (ft'  -  ft")  =  W  (Pv  -  P2)  (ft1  -  ft")  where  P'  =  />,  -  />,. 

The  value  of  ft'  —  ft"  also  must  correspond  to  the  given  range  of 
pressure.  This  last  designation  is  necessary  because  ft'  —  ft"  changes 
in  value  with  changing  pressure,  as  is  shown  on  page  20.  TV'  may 
also  be  found  directly  from  the  results  given  on  page  18  by  graphic 
interpolation,  or  from  the  diagram  of  .3'  —  ft"  by  multiplying  the 
ordinate  value  corresponding  to  the  difference  between  two  pressures 
by  W1  '.  All  these  methods  give  of  course  essentially  the  same  results  ; 
they  were  used  to  verify  one  another  in  the  tables  given  below. 

Among  the  other  quantities  involved  in  the  equation,  the  volumes, 
being  found  by  weighing  quantities  of  mercury  determined  by  the 

1  For  a  table  of  formulae  giving  the  permissible  abbreviations  of  equations 
involving  small  quantities  in  the  presence  of  large  ones,  the  reader  is  referred  to 
Nernst  and  Schonfliess,  Math.  Behand.  der  Naturwiss.,  p.  303  (1895). 


22  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

exceedingly  sensitive  electrical  contact,  can  be  estimated  with  great 
accurac}'.  For  the  pressures,  on  the  other  hand,  we  have  had  to 
depend  chiefly  upon  the  hydraulic  dial  gauge  made  and  guaranteed  by 
Schaeffer  and  Budenberg.  In  view  of  the  extensive  experience  of 
these  manufacturers  and  the  fact  that  the  gauge  is  vouched  for  by  the 
Socie"te  Genevoise  it  seemed  hardly  possible  that  we  could  improve 
upon  the  accuracy  of  their  work.  The  gauge  registers  as  far  as  a 
thousand  atmospheres,  and  has  only  a  very  small  temperature  coeffi- 
cient, according  to  their  testimony  and  our  careful  trial.  We  tested 
this  by  means  of  our  new  liquid  manometer,  described  on  page  41, 
keeping  the  latter  constant  in  temperature  and  varying  the  temperature 
of  the  dial  gauge.  The  temperature  of  the  room  used  for  the  experi- 
ments varied  ordinarily  but  little  from  20°,  hence  no  trouble  could 
have  arisen  from  change  of  temperature,  even  had  the  coefficient  been 
considerable. 

Several  other  indications  point  to  the  accuracy  of  the  gauge.  For 
example,  the  great  regularity  to  be  seen  in  the  various  curves,  particu- 
larly in  that  representing  /?'  —  ft",  points  toward  consistency  in  the 
indications. 

A  number  of  comparisons  of  the  gauge  with  known  weights  placed 
at  the  end  of  the  lever  arm  of  the  press  confirmed  to  some  degree  this 
conclusion.  In  order  wholly  to  eliminate  friction,  and  thus  test  this 
method  more  thoroughly,  a  rotary  piston  might  have  been  provided. 
This  change  would  however  have  involved  a  fundamental  dismantling 
of  the  apparatus,  an  act  which  at  present  we  were  not  willing  to  per- 
form. Yet  another  indication  of  the  accuracy  of  the  gauge  is  found  in 
the  essential  agreement  of  our  work  upon  water,  described  later,  with 
the  work  of  others. 

After  the  work  was  completed,  our  gauge  was  returned  to  Schaeffer 
and  Budenberg,  in  order  to  be  thoroughly  tested  anew.  Their  report 
was  very  satisfactory,  indicating  inessential  errors  in  the  lower  part  of 
the  scale,  and  giving  the  error  at  500  atmospheres  as  only  0.5  atmo- 
sphere. 

Whatever  may  have  been  the  error  of  the  gauge,  the  results  are  ac- 
curate relatively  to  one  another ;  moreover,  they  may  be  easily  cor- 
rected at  any  future  time  with  the  help  of  the  liquid  manometer 
already  mentioned. 

In  view  of  the  facts  above  stated,  it  seems  certain  that  the  possible 
inaccuracies  of  the  gauge  must  be  so  small  as  to  affect  only  the  second 
differential  coefficient,  and  not  the  average  value  of  the  compressibility. 
Hence  even  if  the  possible  errors  in  the  gauge  were  never  found,  the 
following  results  would  be  significant. 


BROMINE  23 

The  substances  whose  compressibilities  we  have  determined  are 
bromine,  iodine,  chloroform,  carbon  tetrachloride,  bromoform,  phos- 
phorus and  water,  while  from  the  results  we  may  also  obtain  the  value 
for  glass  and  a  qualitative  indication  of  the  compressibility  of  liquid 
chlorine.  In  every  case  the  temperature  was  20°.  Further  details 
are  best  discussed  under  the  individual  experiments. 

BROMINE. 

Two  samples  of  bromine  were  used.  The  first  specimen  (used  in 
all  but  the  last  series)  was  prepared  by  the  usual  calcic  bromide 
method  of  Stas.  It  was  subjected  to  an  initial  distillation,  was  dried 
by  means  of  phosphorus  pentoxide,  and  twice  redistilled,  but  was  not 
wholly  free  from  dissolved  air.  Sample  two  (2)  was  an  especially 
pure  specimen  which  had  been  prepared  by  Richards  and  Merigold l 
for  their  work  on  the  atomic  weight  of  uranium.  It  was  dried  over 
phosphorus  pentoxide  and  redistilled.  The  air  was  expelled  by  boil- 
ing just  before  use. 

The  equation  for  the  calculation  of  the  compressibility  shows  that  it 
is  necessary  to  know  accurately  the  specific  gravity  of  the  substance 
under  examination.  Thorpe 3  found  as  the  specific  gravity  of  bromine 
at  o°  (water  at  4°  being  the  standard)  the  value  3.1882.  Pierre* 
found,  with  the  same  standard  and  temperature  a  value,  3.18721.  He 
found  also  that  between  —  7°  C.  and  60°  C.  the  expansion  formula  is 

V=  i  -f  .001  038  18  t  -f  .000001  711  4  /*  -f  .000000005447  **• 

The  average  of  the  values  of  these  two  experimenters,  viz.,  3.1877, 
was  taken  as  the  density  (o°/4°),  and  with  this  as  a  basis  the  value  at 
20°  C.  was  obtained  by  the  use  of  Pierre's  formula.  The  result  is 
3.120  (20°/4°),  and  this  value  was  used  in  the  calculations 
below. 

There  are  given  below  the  essential  data  and  results  of  five  series  of 
experiments  upon  bromine,  made  with  two  different  portions  of  ma- 
terial and  two  different  jackets. 

In  series  i,  2,  3  and  4,  the  weight  of  bromine  was  7.504  grams, 
corrected  to  vacuum,  and  the  containing  thin  bulb  weighed  TV"  =  0.72 
gram.  In  series  5  the  bromine  (the  second  sample,  free  from  dis- 
solved air)  weighed  12.649  grams  (in  vacuum)  and  the  glass  bulb 
weighed  iv"  =  i.io  grams. 

1  Proc.  Am.  Acad.,  37,  387  (1902). 

2Journ.  Chem.  Soc.,  37,  172  (1880). 

3  Ann.  de  Chtm.  et  Phys.  (3),  20,  45  (1847). 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


DATA  FOR  COMPRESSIBILITY  OF  BROMINE.     (2O°C.,  HYDROGEN  SCALE.) 


No.  of 
Series. 

No.  of 
Jacket. 

Observed 
Pressure 

kg./cnf*. 

Actual 
Mercury 
Added  =  w. 

Mercury 
Added  in  Ab- 
sence of  Bro- 
mine =&>' 

Correction 
for  Glass  Bulb 
=0.000007  6  it/ 

Total  Change  of 
Volume  of 
Bromine  Minus 
that  of  Mercury 
(P—P')P.   Percent. 

46 

O 

O 

O 

[0.273  =  a,] 

I 

I 

226 

0.391 

0.085 

O.OOIO 

i.  216 

442 

0.818 

0.182 

O.OO2I 

2.232 

624 

I.I47 

0.259 

0.0031 

3.007 

2 

I 

68 

0 

0 

0 

[0.392  =  a,] 

223 

0.334 

0.073 

0.0009 

I-I95 

392 

0.669 

0.150 

0.0017 

1.991 

565 

0-995 

0.224 

0.0027 

2.765 

3 

1 

60 
206 

0 

0.320 

0 

0.069 

0 

0.0008 

[0.350  =  a,] 

1.  121 

369 

0.649 

0.143 

0.0017 

1.910 

543 

0.983 

0.219 

0.0027 

2.700 

4 

II 

47 

o 

o 

o 

[0.278  =  0,] 

143 

0.242 

0.059 

0.0005 

0.844 

251 

0.486 

0.127 

O.OOII 

1.384 

375 

0.742 

O.2O2 

0.0017 

1.940 

496 

0.992 

0.273 

0.0024 

2.492 

5 

II 

69 

0 

0 

0 

[o.4oo  =  a5] 

no 

0.157 

0.025 

0.0003 

0.640 

162 

0.334 

0.058 

0.0008 

0.905 

356 

0.643 
0.984 

0.113 
0.176 

0.0014 
0.0034 

1.876 

As  will  be  observed,  the  pressures  of  the  starting  points  of  these 
five  series  vary  considerably.  In  order  to  bring  them  to  comparable 
conditions,  we  resorted  to  the  following  method  :  The  first  series, 
that  with  the  lowest  starting  point,  was  plotted  with  "  total  percentage 
changes  of  volume  of  bromine  minus  those  of  mercury  "  in  the  direc- 
tion of  ordinates  and  the  pressures  corresponding  to  these  volume 
changes  as  abscissas.  The  portion  of  the  curve  below  46  atmospheres 
was  extrapolated.  Let  us  call  this  curve  one.  To  plot  the  results 
of  series  2,  for  example,  we  found  the  point  on  curve  one,  which 
corresponded  to  the  initial  pressure  (68)  of  (2)  ;  and  its  ordi- 
nate  gives  the  amount  at  which  must  be  added  to  the  ordinates 
calculated  for  higher  pressures  before  the  loci  of  series  2  could  be 
plotted. 

In  other  words  an  is  the  volume,  constant  within  each  series, 
which  must  be  added  to  each  member  of  the  series  in  order  to  reduce 
them  all  to  the  same  origin.  It  is  found  exactly  as  in  the  case  of 
mercury  already  discussed,  being  the  ordinate  corresponding  to  the 
initial  pressure  of  each  series,  measured  on  the  curve  of  Series  I.  By 
adding  this  quantity  an,  all  the  series  are  superposed  at  their  lowest 
pressures,  and  the  resulting  curve  begins  at  the  origin  of  pressure  and 


BROMINE  25 

of  volume  change.  As  has  been  said,  that  part  of  the  curve  below  46 
atmospheres  is  extrapolated,  but  an  error  occurring  in  it  could  have  no 
effect  on  the  curve  above,  for  this  depends  entirely  upon  the  actual 
observations.  Since  the  calculation  is  somewhat  complicated,  it  may 
be  well  to  state  that  it  was  performed  from  beginning  to  end  by  each 
of  the  authors  independently  on  different  kinds  of  coordinate  paper, 
with  precisely  similar  results.  The  plot  being  40  centimeters  high 
and  33  centimeters  wide,  a  considerable  degree  of  accuracy  was  ob- 
tained. It  was  easy  to  distinguish  0.02  centimeter  or  1/2000  of  the 
maximum  values. 

Thus  the  quantity  given  in  the  last  column  of  the  preceding  table, 
plotted  in  the  direction  of  ordinates  on  the  curve  marked  bromine  in 
the  chart  is 


From  the  curve  it  is  at  once  clear  that  the  compressibility  decreases 
rapidly  as  the  pressure  increases.  In  the  table  below,  the  values  of 
ft  —  /9'  are  given  for  each  hundred  kilograms  per  square  centimeter  ex- 
pressed in  fractions  of  the  original  volume.  The  value  between  o  and 
loo,  being  partly  extrapolated,  is  enclosed  in  brackets.  These  values 
were  taken  directly  from  the  curve. 

COMPRESSIBILITY  OF  BROMINE  AT  20°  C. 


Range  of  Pressure 
(kg./cm'.) 

(/3-/5')ro-«. 

Compressibility 
of  Bromine  =  (J. 

0-100 
100-200 
200-300 
300-400 
4OO-5OO 
5OO-6OO 

[57.5] 
52.5 
48.0 
46.5 
44-5 
42.8 

[0.0000613] 
0.0000563 
0.0000527 
0.0000502 
0.0000481 
0.0000464 

Thus  the  compressibility  of  bromine  is  about  sixteen  times  as  great 
as  that  of  mercury  at  low  pressures.  The  difference  of  temperature 
(3°)  accounts  in  part  for  the  difference  between  these  results  and  the 
preliminary  ones  given  on  page  10. 

IODINE. 

In  order  to  prepare  suitable  material,  "chemically  pure"  iodine 
was  mixed  with  pure  potassium  iodide,  the  two  being  finely  ground, 
and  the  iodine  was  sublimed,  twice  in  succession. 


26  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

As  before,  it  was  important  to  know  accurately  the  specific  gravity 
of  the  substance  at  20°  .  Gay  Lussac  l  found  the  value  4  .  948  (i7°/i7°) 
and  this  reduced  to  (i7°/4°)  gives  a  value  4.942.  Billet2  found  the 
following  values  : 

Temperature  .................  40.3°  60°  79.6°  89.8° 

Specific  gravity  .............     4-9i?3  4.886  4.858  4.841 

but  unfortunately  it  is  not  evident  whether  these  values  are  based  on 
water  at  4°,  or  at  some  other  temperature.  We  can,  however,  obtain 
the  inclination  of  the  curve  from  his  results  and  plot  a  parallel  curve 
passing  through  the  value  obtained  by  Gay  Lussac.  The  density  thus 
obtained  is  4.938  (2O°/4°).  The  value  used  in  the  calculations 
was  4.94. 

The  method  employed  for  determining  the  compressibility  of  iodine 
was  essentially  that  used  in  the  bromine  experiments.  The  question 
of  the  isolation  of  the  iodine  from  contact  with  the  surrounding  mer- 
cury was,  however,  even  more  perplexing  than  with  bromine.  The 
problem  was  finally  solved  according  to  the  following  method.  Two 
small  bulbs,  similar  to  those  used  with  bromine,  were  prepared  (A 
and  B)  .  Into  A  was  put  a  saturated  solution  of  iodine  in  water,  a 
few  wisps  of  glass  wool,  and  a  small  quantity  of  solid  iodine.  Into 
B  was  put  a  saturated  solution  of  iodine  in  water  and  a  large  quan- 
tity of  iodine.  Both  were  sealed  and  subjected  to  quantitative  com- 
pression. The  glass  wool  served  to  hold  the  small  bits  of  iodine  at 
various  positions  throughout  the  solution,  thus  facilitating  the  speed 
of  any  possible  shift  in  the  solubility-equilibrium  when  the  pressure 
changed. 

If  there  are  a  grams  of  water  and  b  grams  of  iodine  in  A,  and  c 
grams  of  water  and  d  grams  of  iodine  in  B,  and  if  volume  change  of 
A  under  pressure  is  m  and  of  B  for  same  pressure  is  n  we  have  the 
following  relationship  : 

a  __  a  -j-  b       m 


where  8  is  a  quantity  of  iodine  which  bears  the  same  relation  to  c 
that  b  bears  to  a  (that  is,  a/6  =  c/d),  and  x  is  the  volume  change 
of  the  water  c  in  tube  B  plus  the  volume  change  of  a  small  quantity 
of  iodine.  8.  Evidently,  then,  (n  —  x)  represents  the  volume  change 
of  the  quantity  of  iodine  (d  —  8).  This  method  is,  of  course,  appli- 
cable in  all  cases  where  the  solid  under  consideration  is  attacked  by 

1  Ann.  de  Chim.,  91,  5  (1814). 

"Jahresbericht,  (1855)  46.^ 


IODINE  27 

mercury.  There  are  two  distinct  reasons  for  the  use  of  mercury  in- 
stead of  the  direct  use  of  the  neutral  liquid  in  the  outer  jacket  —  first, 
because  the  transmission  of  the  heat  of  compression  to  the  surrounding 
water  when  mercury  is  used  is  quick  and  certain,  and  second  be- 
cause the  compressibility  of  mercury  is  so  small  that  any  slight  change 
in  volume  due  to  a  slightly  different  placing  of  the  stopper  cannot  in- 
fluence the  results.  With  more  compressible  liquids  the  error  thus 
introduced  might  be  considerable. 

The  special  advantage  of  the  method  in  connection  with  iodine  lies 
in  the  fact  that  it  obviates  all  possible  error  due  to  a  change  in  the 
solubility  of  iodine  in  water  with  change  of  pressure.  There  are,  it  is 
true,  two  possible  sources  of  error  which  it  does  not  guard  against : 
first,  the  solubility  of  water  in  iodine ;  and  secondly,  the  change  in  that 
solubility  with  change  of  pressure.  When  we  consider,  however,  the 
fact  that  liquids  usually  dissolve  solids  to  a  greater  extent  than  solids  dis- 
solve liquids,  and  remember  that  iodine  is  soluble  in  water  to  the  extent 
of  only  about  one  part  in  three  thousand,  it  is  hard  to  believe  that  either 
of  these  influences  could  have  an  appreciable  effect  upon  the  results  ob- 
tained below.  Moreover,  since  the  compressibilities  of  iodine  and  water 
are  of  the  same  order  of  magnitude,  the  amount  of  water  dissolved  by  the 
iodine  must  be  great  before  any  difference  would  appear  in  the  result. 
In  obtaining  the  weight  of  iodine  and  water,  the  method  used  was  to 
weigh  the  bulbs  full  of  water  and  iodine ;  then  break  them  under  a 
solution  of  potassium  iodide  and  titrate  the  iodine  with  recently  stan- 
dardized thiosulphate.  The  glass  particles  were  then  collected,  dried 
and  weighed,  and  the  weight  of  the  water  was  found  by  difference. 
The  small  amount  of  iodine  dissolved  in  the  water  was  neglected  as 
too  slight  to  cause  appreciable  effect.  For  the  purpose  of  standard- 
izing the  sodic  thiosulphate  solution,  3.080  grams  of  dry,  recently  re- 
sublimed  iodine  were  dissolved  in  potassium  iodide  solution  and  diluted 
to  a  volume  of  0.2509  liter.  This  was  titrated  against  the  approxi- 
mately decinormal  thiosulphate  solution.  The  results  are  given  below, 
burette  corrections  having  been  applied.  As  an  average  of  three 
closely  agreeing  determinations,  44.29  milliliters  of  the  thiosulphate 
solution  required  25.92  milliliters  of  the  iodine  solution.  Therefore 
one  milliliter  of  the  thiosulphate  solution  was  equivalent  to  0.007246 
gram  of  iodine. 

The  total  quantity  of  iodine  in  bulb  A  required  22.67  milliliters  of 
the  thiosulphate  solution,  therefore  the  weight  of  iodine  present  must 
have  been  0.1643  gram. 

The  iodine  in  bulb  B  was  dissolved  in  potassium  iodide  and  diluted 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


to  0.2509  liter,  and  as  an  average  of  three  closely  agreeing  titrations 
17.32  milliliters  of  this  solution  required  45.45  milliliters  of  the  thio- 
sulphate  solution.  Therefore  the  number  of  grams  of  iodine  in  B  was 
4.7723  grams.  The  weights  of  the  glass  in  the  two  bulbs  A  and  B 
were  respectively  0.91  and  0.97  gram,  and  the  weights  of  water  pres- 
ent in  each  were  respectively  2.674  an(^  I-S39  grams. 
In  both  cases  jacket  II  was  used. 

COMPRESSIBILITY  DATA  FOR  IODINE. 
Bulb  A. 


Series. 

Observed 
Pressure. 

Total  wt. 
of  He 
Added. 

Correction 
for 
Jacket. 

Correction 
for 
Bulb. 

Corrected 
wt.of 
Hg  Added. 

m' 

6 

53 
173 
302-5 

0 

0.2438 
0.5013 

0.0740 
0.1540 

0.0008 
O.OOI7 

.1706 
•349° 

O 
0.46 
0-95 

7 

90 
217 
302.5 

0.0000 

0.2584 
0.4278 

0.0783 
O.I3I3 

o.oooS 
0.0014 

.1809 
.2979 

O 

0.45 
0.81 

Bulb  B. 


8 

88 

o 

o 

233 

0.2502 

0.0893 

O.OOIO 

.1619 

0.428 

384 

0.5003 

0.1813 

O.OO2I 

.3211 

0.848 

9 

in 

o 

0 

248 

0.2365 

0.0840 

O.OOIO 

•1535 

0.405 

384 

0.4633 

0.1670 

0.0019 

.2982 

0.788 

Under  m1  is  given  the  percentage  change  in  volume  of  2.674  grams 
of  water  and  0.1643  gram  °f  iodine  minus  the  percentage  decrease  of 
an  equal  volume  of  mercury.  (6)  and  (7)  are  two  series,  the  first 
made  by  adding  small  quantities  of  mercury,  the  second  by  taking  out 
small  quantities  after  the  highest  pressure  had  been  reached.  This 
method  of  procedure  is  especially  desirable  with  solids,  as  it  will  af- 
ford indication  of  a  permanent  alteration  in  the  volume  of  the  solid 
under  pressure,  if  such  alteration  occurs.  It  also  gives  valuable  proof 
of  the  absence  of  leakage  from  the  glass  jacket. 

Under  «'  is  given  the  percentage  decrease  in  the  volume  of  1.829 
grams  of  water  and  4.7723  grams  of  iodine  minus  the  percentage  de- 
crease of  an  equal  volume  of  mercury.  (8)  and  (9)  are  two  series 
made  as  before,  one  by  adding  mercury,  the  other  by  taking  out  small 
quantities  of  mercury.  By  adding  the  compression  of  mercury,  m  and 
n  are  respectively  obtained  from  m'  and  »'. 

Making  the  calculation  indicated  in  the  earlier  part  of  the  remarks 
on  iodine,  we  have  in  the  equation  8  =  t>c/a,  by  substituting  the  values 
found, 
<)  =  0.1643  x  1-829/2.674  =  0.1124  gram  and  (d  —  3)  ==  4.66  grams. 


CHLOROFORM  AND  CARBON  TETRACHLORIDE 


This  represents  the  quantity  of  iodine,  the  compression  of  which 
was  measured.  Its  volume  is  0.943  niilliliters,  or  0.348  of  the  volume 
of  its  bulb. 

Now  x  =  me  I  a  =  0.684  m'  From  the  values  of  m  given  under  the 
work  on  bulb  A  the  values  of  x  were  calculated  and  plotted  as  ordi- 
nates  with  the  corresponding  pressure-differences  as  abscissae.  This 
was  called  the  curve  of  x.  Then  the  values  found  in  the  work 
on  bulb  B  were  also  plotted,  using  values  n  as  ordinates  and  pressure- 
differences  as  abscissae.  The  curves  were  both  extrapolated  in  order 
to  pass  through  the  origin.  In  order  to  economize  space,  the  curves 
themselves  are  not  given  here,  but  in  the  table  below  are  given  all  the 
data  needed  to  reproduce  them,  (n  —  x)/o.^8P  is  the  compressi- 
bility of  the  iodine. 

COMPRESSIBILITY  OF  IODINE. 


Abscissa 
(Pressures). 

Ordinates. 

{»-*} 

(0  —  0')io«for 
Each  Successive 
100  Pressure  Units. 

/rxo« 

Curve  of  n. 

Curve  of  x. 

100 
200 
300 

[0.346] 
0.680 
1.005 

[0.300] 
0.590 
0.872 

[0.046] 
0.090 
0-133 

[9-6] 
8.9 
8.6 

[51 

12. 

Thus  the  compressibility  of  iodine  is  far  less  than  that  of  bromine, 
being  only  three  times  that  of  mercury.  This  result  does  not  pre- 
tend to  any  considerable  degree  of  accuracy ;  the  small  amount  of  ma- 
terial used  and  the  complication  of  the  method  preventing  great  pre- 
cision. It  is,  nevertheless,  sufficiently  certain  for  the  present  purpose, 
and  accordingly  further  work  upon  iodine  was  postponed. 

CHLOROFORM  AND  CARBON  TETRACHLORIDE. 

These  substances  were  next  studied,  with  the  justifiable  hope  that 
their  behavior  might  furnish  some  clue  as  to  the  compressibility  of 
chlorine.  In  order  to  purify  the  former  material,  commercial  chloro- 
form was  shaken  repeatedly  with  strong  sulphuric  acid  and  then  with 
successive  portions  of  water.  It  was  afterwards  dried  with  calcium 
chloride  and  twice  distilled.  During  the  second  distillation  two  thirds 
of  the  product  passed  over  between  61.2°  and  61.3°  C.,1  and  from  this 
fraction  the  material  for  the  compression  experiments  was  taken. 

As  before,  accurate  knowledge  of  the  density  is  needed.  Thorpe1 
found  for  the  specific  gravity  of  chloroform  the  value  1.5264  at  o°/4°  ; 
and,  under  the  same  conditions  of  temperature,  Pierre5  found  1.5252. 

1The  barometric  pressure  was  759  mm.  and  the  thermometer  reading  was  cor- 
rected for  the  temperature  of  the  projecting  column  of  the  thermometer. 
2Journ.  Chem.  Soc.,  37,  196  (iSSo). 
"Compt.  Rend.,  27,  213  (1848). 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


Moreover  Perkin1  found  1.5008  at  i5°/i5°  and  1.4849  at  25°/25°. 
These  values  of  Perkin's  reduce  to  1.4993,1 5 °/4°,  and  1.4801,  25°/4°. 
If  the  values  of  these  three  observers  be  plotted  the  interpolated  value 
for  the  density  at  2O°/4°,  is  found  to  be  1.490. 

In  order  to  obtain  the  other  compound  of  chlorine  in  a  pure  state, 
tetrachlormethane  of  commerce  was  twice  distilled,  and  the  fraction 
coming  over  between  76.6°  and  76.8°  C.  (cor.)  was  used.  This  sub- 
stance has  a  higher  specific  gravity  than  chloroform.  Thorpe2  found 
(o°/4°)  1.63195  and  a  volume  increase  of  2.45  per  cent,  at  20°. 
These  values  give  1.593  (2O°/4°)' 

The  method  of  determining  the  compressibility  of  these  substances 
was  precisely  similar  to  that  used  in  the  case  of  bromine.  The  glass 
jacket  II,  containing  the  maximum  amount  of  437  grams  of  mercury, 
was  used  in  each  of  the  four  series  given  below.  The  weight  of  the 
chloroform  was  5.354  grams,  hence  its  volume  was  3.590  milliliters, 
while  the  corresponding  data  in  the  case  of  the  carbon  tetrachloride 
were  6.970  grams  and  4.403  milliliters.  The  weights  of  the  two  thin 
bulbs  were  respectively  0.55  and  1.06  grams.  Series  13  was  obtained 
by  taking  out  mercury  instead  of  adding  it.  Its  perfect  agreement 
with  series  1 2  shows  that  the  apparatus  was  in  excellent  order. 
DATA  FOR  CHLOROFORM  AND  CARBON  TETRACHLORIDE. 


Series. 

Observed  Pressure  P. 

Chloroform.  Weight 
of  Hg.  Added. 

Total  Percentage. 
Change  of  Volume 
Minus  that  of  Mercury 
=  (B-B')P 

kg./cma. 

grams. 

per  cent. 

IO 

53-5 

O 

0-475  =  «io 

201.5 

0.684 

1.691 

374-5 

1.398 

2.938 

574-5 

2.II4 

4.162 

II 

88 

O 

0-775  =  0ii 

181 

0.442 

1-565 

293 

0.909 

2.381 

492 

1.658 

3.670 

637.5 

2.167 

4-537 

Carbon  tetrachloride. 


12 

56 

0 

0.499=^!, 

159 

0.578 

1.367 

250 

1.063 

2.093 

324 
410 

1-839 

2.657 
3-237 

13 

248 

1.048 

2.068  =  als 

410 

1.839 

3-237 

This  table  contains  all  the  data,  in  addition  to  the  previously  re- 
corded figures,  necessary  for  computing  the  compressibilities  of  the 

^ourn.  Prakt.  Chem.  (2),  32,  573  (1885). 
2Journ.  Chem.  Soc.,  37,  198  (1850). 


CHLOROFORM  AND  CARBON  TETRACHLORIDE 


two  liquids.  The  last  column,  precisely  similar  to  the  corresponding 
column  in  the  preceding  data  concerning  bromine,  gives  the  total 
change  of  volume  in  milliliters  of  100  milliliters  of  liquid,  caused  by 
the  application  of  each  pressure,  minus  the  total  change  in  volume  of 
the  same  volume  of  mercury  caused  by  the  same  pressure.  The  cor- 
responding curves  are  plotted  in  the  diagram  Fig.  5.  From  the  aver- 
age of  several  large  plottings  of  this  kind  on  two  varieties  of  coordinate 
paper,  the  values  of  the  compressibilities  of  the  two  liquids  contained 
in  the  following  table  were  obtained. 

COMPRESSIBILITIES  OF  CHLOROFORM  AND  CARBON  TETRACHLORIDE. 


Range  of  Pressure. 
kg./craa. 

Chloroform. 
O-jS')io». 

CC14  (/S-|8')io«. 

Compressibility 
of  Chloroform 
(/3io«) 

Compressibility 
of  Carbon  Tetra- 
chloride  (0io«). 

O-IOO 
IOO-2OO 

200-300 
300-400 
400-500 
500-600 

l$? 
ftj 

61.7 
57-5 

[86.2] 

82.8 

78.2 
70.5 
65.0 

61.1 

[91.4] 
86.4 
77-2 
70.2 

65.3 
61.1 

te] 

82.0 

74.2 

68.6 
64.7 

As  before,  the  curve  below  100  atmospheres  is  partly  extrapolated, 
hence  the  first  figure  is  uncertain  in  each  case.  The  values  are  very 
consistent  and  are  not  far  different,  for  the  two  liquids,  each  being 
about  one  and  a  half  times  as  compressible  as  bromine.  It  is  remark- 
able and  an  interesting  fact  that  although  the  carbon  tetrachloride  is  at 
first  slightly  less  compressible  than  chloroform,  above  200  atmos- 
pheres, the  relative  magnitudes  are  reversed,  since  the  compressibility 
of  the  former  substance  diminishes  less  rapidly  than  that  of  chloroform 
with  increasing  pressure.  This  point  will  be  referred  to  again. 

It  is  worthy  of  note  that  Grassi  found  the  compressibility  of  chloro- 
form to  increase  with  increasing  pressure  below  10  atmospheres. 
Whether  this  is  an  inaccurate,  observation,  or  whether  an  anomalous 
behavior  really  occurs  at  low  pressures,  it  is  impossible  to  ascertain 
without  further  data.  It  is  our  intention  to  pursue  the  question. 
Since  Grassi's  values  were  obtained  at  12°  they  are  not  directly  com- 
parable with  ours.  In  any  case,  the  present  observations  establish 
beyond  doubt  the  fact  that  at  high  pressures  chloroform  decreases  in 
compressibility  with  increasing  pressure  in  the  usual  way. 

From  the  great  compressibility  of  these  liquids,  consisting  chiefly  of 
chlorine,  and  possessing  boiling  points  not  far  from  bromine,  it  seems 
certain  that  chlorine  must  be  much  more  compressible  than  bromine 
under  similar  circumstances.  In  order  to  obtain  further  light  upon 
this  important  question,  which  cannot  be  easily  answered  by  direct  ex- 


32  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


t 


ESSURE  100 


ZOO  300 

FIG.  5. 


BROMOFORM  3^ 

periment,  we  thought  it  worth  while  to  determine  the  compressibility 
of  bromoform,  because  of  its  close  analogy  to  chloroform. 

BROMOFORM. 

Merck's  "chemically  pure  "  bromoform  boiling  between  150.3°  and 
150.5°  l  was  used.  Perkin*  found  the  specific  gravity  of  this  substance 
to  be  2.903  at  15715°,  and  2.883  at  25°/25°.  These  values  reduce 
to  2.900  at  i5°/4°  and  2.875  at  25°/4°,  from  which  by  interpolation 
we  obtain  the  value  2.888  at  2O°/4°. 

The  determination  of  the  compressibility  of  bromoform  was  made 
in  the  special  jacket  (No.  IV)  devised  for  the  determination  of  the 
compressibilities  of  liquids  which  do  not  attack  mercury.  It  was. 
found  during  the  course  of  the  experiment  that  a  slight  action  between 
mercury  and  bromoform  had  nevertheless  taken  place ;  yet  the  results 
can  hardly  have  been  vitiated  to  an  extent  exceeding  one  per  cent., 
and  for  the  purpose  of  this  part  of  the  work,  namely,  the  fixing  of  the 
position  of  the  compressibility  of  chlorine  with  relation  to  those  of  the 
other  halogens  this  degree  of  accuracy  is  all  that  is  needed.  The 
method  of  experimentation  is  evident  from  the  following  sketch~and 
descriptions. 

The  jacket  full  of  mercury  weighed  291.6  grams,  while  the  weight 
of  the  bromoform,  partly  replacing  the  mercury,  was  54.63  grams. 

DATA  FOR  BROMOFORM. 


Series. 

Observed  Pressure. 

Total  Hg  Added. 

Percentage  Change  in 
Volume  of  Bromoform  Minus 
that  of  Mercury  =  (/3—  /3')/». 

14 

£, 

360 

0 

1.546 
3-591 

0.145 
0.727 
1.494 

From  these  data,  plotted,  the  compressibility  results  for  bromoform 
are  readily  found  to  be  the  following : 


COMPRESSIBILITY  OF  BROMOFORM. 


Range  of  Pressure  kg./cm*. 

(/3-/3')io«. 

0.10«. 

O-IOO 
IOO-2OO 
2OO-3OO 
300-400 

45-3 
42.0 
38.8 
36.8 

49-1 

45-8 
42.5 
40-5 

Thus  the  compressibility  of  bromoform  is  somewhat  less  than  that 
of  bromine,  being  about  thirteen  times  as  great  as  that  of  mercury. 
Bromoform  is  only  about  half  as  compressible  as  chloroform. 

1  Corrected  for  exposed  column,  under  760  mm.  pressure. 

2  Journal  Prakt.  Chem.  (2),  32,  523  (1885). 


34 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


THE  PROBABLE  COMPRESSIBILITY  OF  CHLORINE. 

It  has  already  been  suggested  that  there  is  good  reason  for  believing 
that  chlorine  is  much  more  compressible  than  bromine.  There  are 
indeed  at  least  three  reasons  for  this  belief,  namely  :  first,  the  fact  that 
chloroform  and  carbon  tetrachloride  are  both  much  more  compres- 
sible than  bromine,  although  their  boiling  points  are  no  lower ;  sec- 
ondly, because  bromoform  is  so  much  less  compressible  than  the 
analogous  chloroform ;  and  thirdly,  because  bromine  is  so  much  more 
compressible  than  iodine,  a  fact  which  leads  one  to  infer  that  chlorine 
would  be  yet  more  so,  because  of  the  well  known  periodicity  of  these 
elements. 

There  are  at  least  two  ways  in  which  a  quantitative  estimate  may  be 
formed  of  the  compressibility  of  chlorine.  Fortunately  the  differences 
between  the  boiling  points  of  chloroform  and  bromoform  (152°  — 
6i°  =  9i°)  is  almost  exactly  the  same  as  the  difference  between  the 
boiling  points  of  chlorine  and  bromine  (60°  —  ( —  32°)=  92°)  ;  or,  to 
express  the  same  relation  in  another  way,  the  boiling  point  of  chlorine 
is  as  much  below  that  of  chloroform  as  that  of  bromine  is  below  that 
of  bromoform.1  Thus  the  effect  of  the  internal  pressure  of  cohesion,  as 
indicated  by  the  different  boiling  point,  upon  the  compressibility  in  the 
former  case  may  be  assumed  to  be  the  same  as  the  known  effect  in  the 
latter  case.  Overlooking  other  minor  differences,  such  as  the  absolute 
temperature  and  the  possibly  varying  effect  of  the  hydrogen  and  carbon 
(which  however  probably  constitute  only  a  small  proportion  of  the 
volume  of  chloroform  and  bromoform) ,  it  may  be  supposed  that  the 
following  equation  holds  approximately  true  : 


a  n 

PCI  =  PCHCIJ  "o 

/3CH  Br3 

From  the  figures  already  given  for  the  variables  in  the  right  hand 
member  of  this  equation,  it  is  easy  to  compute  the  following  values 

1  The  boiling  points  of  the  halide  substitution  products  of  methane  are  inter- 
esting in  their  regularity.  Each  substitution  of  bromine  for  chlorine  involves  a 
rise  of  boiling  point  of  about  28°.  This  regularity,  which  is  shown  in  the  table 
below,  supports  the  method  of  approach  used  above. 


Substance,     j  Boiling  Point. 

Substance. 

Boiling  Point. 

Difference. 

&. 

CHC13 

_32° 

+  77 
+  61 

Br, 
CBr, 
CHBr, 

+    60 
+  I89 

+  152 

92° 
112 
91 

=   4X28 
=   3X30 

CH,C1, 

+  42 

CHjBr, 

+    97 

55 

=   2X27 

CH.C1 

—  22 

CH3Br 

+     5 

27 

=  27 

CH4 

CHt 

o 

CHLORINE 


35 


for  the  left  hand  member  for  each  successive  hundred  units  of  pressure, 
namely:  114,  106,  96,  87,  81.  Similar,  though  somewhat  lower 
results  are  found  if  an  additive  instead  of  a  proportional  relation  is 
assumed. 

Another  method  of  computing  any  property  of  chlorine  is  by  extra- 
polating that  property  of  bromine  and  iodine. 

In  some  cases,  such  as  the  atomic  weights  and  volumes,  the  relation 
is  almost  linear ;  in  such  cases  extrapolation  of  this  kind  is  moderately 
accurate  in  its  results.  Compressibility,  being  a  volume  function,  may 
also  be  assumed  to  vary  in  approximately  linear  fashion.  Upon  this 
assumption,  the  compressibility  of  chlorine  would  be  that  of  bromine 
plus  the  difference  between  that  of  bromine  and  iodine.  The  values 
thus  obtained  agree  surprisingly  well  with  those  given  above,  as  may 
be  seen  from  the  following  table. 

PROBABLE  COMPRESSIBILITY  OF  CHLORINE  AT  20°  C. 


Range  of  Pressure. 
Kg.  /cm'. 

Calculated  from 
Chloroform  and 
Bromoform. 
/Sio-«= 

Calculated  from 
Bromine  and 
Iodine  0io-»= 

Average  ft.  10* 

O-IOO 

114 

109 

112 

IOO-2OO 

106 

109 

107 

2OO-3OO 

& 

101 

98 

300-400 

87 

87 

400-500 

81 

81 

This  curve  is  plotted  in  a  dotted  line  on  the  diagram  (Fig.  5).  It 
makes  no  pretensions  to  accuracy,  but  serves  to  give  an  approximate 
idea  of  the  probable  magnitude  of  the  quantity  in  question.  It  will  be 
seen  that  chlorine  is  probably  nearly  twice  as  compressible  as  bromine 
and  thirty  times  as  compressible  as  mercury. 

PHOSPHORUS. 

The  material  used  was  the  purest  commercial  pale  yellow  phophorus, 
which  was  fused  under  water  and  cast  into  sticks  of  suitable  size. 
These  sticks  were  cut  into  lengths  of  about  half  a  centimeter  each,  in 
order  to  disclose  occasional  cavities.  All  imperfect  pieces  were  of 
course  rejected.  The  specific  gravity,  according  to  the  recent  deter- 
minations of  Pisati  and  de  Francius,1  is  1.823.  The  phosphorus  was 
weighed  under  water  after  washing  with  alcohol  and  ether  and  drying. 

Phosphorus  attacks  mercury  too  vehemently  to  be  immersed  directly 
in  the  mercury  of  the  glass  jacket.  It  was  therefore  packed  into  a 
thin  glass  tube  containing  water ;  and  in  order  to  be  handled  more 

1  Berichte  d.  deutsch  ch.  Ges.  8,  70  (1875). 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


readily,  this  tube  was  closed  with  a  slightly  lubricated  stopper  contain- 
ing a  single  fine  orifice.  This  tube  thus  filled  was  attached  to  a  small 
hook  on  the  inside  of  the  glass  jacket,  a  profitable  precaution  which 
prevented  the  inner  tube  from  rising  by  its  great  buoyancy  and  cutting 
off  the  electrical  connection,  as  well  as  facilitated  the  filling  of  the 
jacket  with  mercury. 

After  adding  successive  amounts  of  mercury  to  the  jacket  thus  filled, 
applying  the  corresponding  pressures,  and  thus  determining  the  pres- 
sure-volume relations  of  this  complex  system,  the  phosphorus  was 
removed,  and  its  place  was  filled  by  precisely  the  same  volume  of 
mercury,  everything  else  remaining  unchanged.  The  compression  ex- 
periments were  then  repeated,  and  the  difference  between  the  two 
series  obviously  gave  at  once  the  difference  of  compression  between 
the  given  volume  of  phosphorus  and  mercury. 

Two  entirely  independent  sets  of  experiments  were  made,  every  de- 
tail of  the  operation  being  repeated.  Their  very  satisfactory  agree- 
ment not  only  shows  that  no  trivial  errors  of  recording  were  made,  but 
also  affords  excellent  evidence  of  the  accuracy  of  the  method.  The 
values  marked  with  asterisks  were  obtained  by  removing  small 
amounts  of  mercury  after  the  maxima  had  been  reached.  Their  ex- 
act coincidence  with  the  appropriate  curves  drawn  through  the  other 
points  showed  that  no  permanent  "  set"  had  been  caused  by  the  appli- 
cation of  the  high  pressures. 

The  results  of  the  two  complete  sets  are  given  below.  The  weight  of 
the  phosphorus  in  the  first  case  was  8.304  grams,  and  in  the  second 
case  8.283  grams. 

Upon  plotting  these  values,  regular  curves  are  obtained  which,  when 

DATA  FOR  COMPRESSIBILITY  OF  PHOSPHORUS  20°  C.  (COR.). 


Series  15  with  Phosphorus. 

Series  16  with  Mercury. 

Pressures 
(kg./cm«.) 

"•aa* 

Same  +  a»  = 
Ordinate  of 
Curve. 

Pressures 
(kg./cm«.) 

Added. 

Same  +  a»  = 
Ordinate  of 
Curve. 

62.5 

o 

[o.242  =  a15] 

95 

O 

[o.265  =  alt] 

197.5 

0.510 

0-753 

217-5 

0-337 

0.602 

338.5 

1.018 

1.260 

350 

0.679 

0.944 

482.5 

1-525 

1.767 

477-5 

0.995 

1.260 

*358.o 
•160.5 

*i.o89 
*o.376 

I-33I 
0.618 

*i95-5 

*0.26l 

0.526 

Series  17  with  Phosphorus. 


Series  1 8  with  Mercury. 


53 

o 

[o.204  =  an] 

65-5 

o 

[o.i83  =  a,g] 

199.5 

0-551 

0-755 

176-5 

0.306 

0.489 

480.0 

1.051 
1-552 

1-255 
1-756 

310 
432 

0.661 
0-973 

0.844 
1.156 

*I78 

*o.474 

0.678 

*I77 

*o.3o6 

0.489 

PHOSPHORUS 


37 


superposed  in  the  usual  manner,  give  very  consistent  values.  The 
averages  are  given  below,  together  with  the  compressibility  of  phos- 
phorus computed  from  them,  for  each  100  units  of  pressure.  The 
quantity  A  —  B  represents  the  value  in  the  large  brackets  of  equation 
(5),  from  which  ft  —  ff  is  easily  calculated. 

COMPRESSIBILITY  OF  PHOSPHORUS. 


Absciss* 
Pressures. 
kg./cm». 

Ordinates. 

A—B. 

O-0')io«  for 
Each  Succes- 
sive xoo  Pres- 
sure Units. 

ft.  I0». 

A  =  Curve 
of  /V 

B  =  Curve 
of  Hg. 

o 

o 

O 

o 

100 
200 
300 

400 

5"0 

0-385 
0-759 
1.124 
1.480 
1.829 

0.280 
0.552 
0.817 
1.074 
1.325 

0.105 
O.2O7 
0.307 
0.406 
0.504 

Si 

16.2 
16.1 
15-9 

20.9 
20.4 
19.9 
19.8 
19.6 

Thus  the  compressibility  of  phosphorus  is  about  half  that  of  water 
and  more  than  five  times  that  of  mercury. 

WATER. 

Four  reasons  make  it  desirable  to  determine  the  compressibility  of 
water.  In  the  first  place,  this  liquid  could  be  accurately  used  in  both 
forms  of  apparatus,  and  hence  could  serve  as  a  certain  means  of  com- 
paring the  results  of  each.  Again,  so  many  investigators  have  de- 
termined this  quantity  that  it  serves  as  an  excellent  means  of  comparing 
our  method  with  those  of  others.  Further,  the  value  obtained  by  our 
present  apparatus  may  at  some  future  time,  by  comparison  with  the 
results  of  an  experimenter  with  a  perfect  pressure  gauge,  serve  con- 
veniently to  determine  by  backward  calculation  the  error  of  our  pres- 
sure-gauge, and  thus  correct  all  the  results  in  this  paper.  Finally,  the 
compressibility  of  water  at  pressures  above  262  atmospheres  seems 
never  to  have  been  determined. 

The  water  used  in  the  determinations  described  below  was  purified 
by  two  successive  distillations,  the  first  one  being  from  permanganate 
solution.  It  was  boiled  just  before  being  used,  to  expel  the  air. 

As  has  been  stated,  its  compressibility  was  determined  in  two  ways, 
first,  by  the  method  used  with  the  bromine;  and  second,  by  the 
method  first  used  with  bromoform,  namely  by  means  of  the  jacket  de- 
vised for  liquids  which  do  not  attack  mercury. 

Three  series  are  recorded  below.  No.  19  was  made  by  the  first 
method,  and  Nos.  20  and  21  by  the  second  method.  The  correspond- 
ing glass  jackets  were  II  and  IV,  containing  when  full  437  and  291.6 
grams  of  mercury  respectively.  The  weights  of  water  were  4.165  and 


209092 


NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 


^8.725  grams  (corrected  to  vacuum)  respectively.  The  weight  of  the 
thin  bulb  in  series  19  was  1.09  grams  —  of  course  none  was  used  in 
Series  20  and  2 1 . 


Series. 

Observed  Pressure. 

Actual  Weight  of 
Mercury  Added. 

Volume  Decrease  in 
Water  Minus  Ditto  in 
Mercury. 

kg./cm'. 

grams. 

per  cent. 

*9 

43 

0 

(0.179  ^a,9) 

137 

0.2778 

0.569 

237 

0.5600 

0.960 

350 

0.8516 

T-356 

20 

20.5 

o 

(  0.084  -^aM) 

118 

1.034 

0.474 

216.5 

2.045 

0.855 

3io-5 

2.991 

1.  212 

406.5 

3-9" 

1-559 

21 

35 

o 

(0.144  -a,,) 

232 

2.053 

0.919 

331 

3.041 

1.292 

These  figures  are  plotted  as  usual  on  the  diagram  (Fig.  5),  and  yield 
a  curve  of  the  same  type  as  the  others,  with  very  few  discrepant  points. 
The  highest  results  of  each  series  falls  exactly  upon  the  curve,  showing 
that  the  methods  give  identical  results  within  the  necessary  limits  of 
error  of  each.  Hence  the  thin  glass  bulb  used  in  Series  19,  as  well  as 
earlier  in  Series  i  to  13,  introduced  no  appreciable  error.  It  is  worthy 
of  note  also  that  the  compressibility  of  a  saturated  solution  of  iodine  in 
water  may  be  computed  from  the  experiments  on  iodine,  and  is  found 
thus  to  be  less  than  one  per  cent,  different  from  that  of  pure  water 
at  each  point  in  the  curve.  The  small  magnitude  of  this  difference 
confirms  both  the  work  and  the  calculation  of  the  iodine  results. 

From  the  curve  given  on  the  diagram  the  compressibility  of  pure 
water  may  be  found  as  follows  : 

COMPRESSIBILITY  OF  WATER. 


Range  of  Pressure  kg./cmf  . 

UMTJ«A 

*iA 

O-IOO 
100-200 
2OO-3OO 
300-400 
400-500 

[40.5] 
39-5 

m 

35-0 

[44-3] 
43-3 
41.0 

Thus  water  is  between  eleven  and  twelve  times  as  compressible  as 
mercury,  and  about  half  as  compressible  as  chloroform. 

Other  experimenters  have  rarely  used  20°  as  their  standard  tempera- 
ture, hence  their  results  must  be  reduced  before  comparison  with  ours. 
Several  investigators  have  shown  that  the  compressibility  of  water 


39 


increases  with  decreasing  temperature,  a  somewhat  unique  phenome- 
non. There  is  no  doubt  that  the  anomaly  is  connected  with  the  anoma- 
lous temperature  coefficients  of  other  properties  of  water,  and  may  be 
supposed  to  be  due  here  also  to  the  increasing  presence  of  a  more 
bulky  polymer  at  lower  temperatures.  With  the  help  of  the  table  given 
on  page  269  of  the  admirable  book  of  Landolt  and  Bornstein  (1894), 
it  is  easily  possible  to  make  an  approximate  correction  for  temperature. 
Corrected  in  this  way  to  20°,  and  also  transposed  from  the  "atmo- 
sphere "  to  the  metric  unit,  some  of  the  values  found  for  the  compres- 
sibility of  water  are  given  in  the  following  table  : 

Thus  our  result  accords  closely  with  the  higher  value  found  by  Tait 
and  with  the  results  of  Pagliani  and  Vicentini,  Avenarius,  Grinaldi, 
Schneider,  and  Rontgen  and  Schumann.  It  is  somewhat  higher  than 
the  values  found  by  Drecker  and  Amagat,  and  the  second  value  found 
by  Tait. 

COMPRESSIBILITY  OF  WATER. 

COMPARISON  OF  WORK  BY  DIFFERENT  EXPERIMENTERS. 


Range 
of  Pressures. 

Investigator. 

/• 

flt0  io*Recip. 
Atmospheres. 

/3,».io« 
Recip.  kg./cm*. 

Rontgen  and  Schneider. 

18.0° 

46.2 

44-3 

Tait. 

12. 

48.0 

44-6 

T,ow 

Tait. 

10. 

44-2 

40.3 

pressures." 

Schumann. 
Drecker. 

I7.I 
2O. 

45-9 
43-8 

43-9 
42.4 

Average,  Pagliani,  Vicentini, 
Avenarius,  Grinaldi. 

2O. 

46.1 

44-6 

O-IOO 

Richards  and  Stall. 

2O. 

45-8 

44-3 

0-262 

Amagat. 

I7.6 

42.9 

41.0 

0-262        i     Richards  and  Stnll. 

2O. 

44-5 

43-1 

The  close  agreement  of  our  value  (44.3)  with  that  accepted  as  the 
most  probable  [46.09  (1000/1033)  =44.6]  by  Landolt  and  Bornstein 
(1894,  page  269),  is  very  satisfactory,  especially  since  the  slight  dif- 
ference of  less  than  one  per  cent,  is  probably  due  to  the  low  pressures 
used  in  obtaining  the  higher  of  the  two  results. 

The  agreement  is  close  enough  to  show  that  the  measurement  of 
pressure  —  the  least  certain  part  of  our  determination  —  must  have 
been  essentially  correct.  This  conclusion  affords  valuable  verification  of 
the  present  measurements  of  all  the  other  substances  as  well  as  of  water. 

THE  HEAT  OF  COMPRESSION. 

It  has  been  already  shown  in  the  early  part  of  this  paper  that  the 
heating  of  the  compressed  material  causes  a  thermal  expansion  so  great 
us  to  cause  the  first  breaking  of  the  galvanic  current  in  the  jacket  to 


40  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

occur  at  a  much  higher  pressure  than  the  true  pressure  corresponding 
to  isothermal  compression.  Since  the  substance  itself  is  the  measuring 
medium,  it  was  thought  possible  that  this  instant  self-heating  effect 
might  afford  a  means  of  avoiding  the  lag  which  any  form  of  thermom- 
eter must  involve,  and  thus  give  a  truer  measure  of  the  adiabatic  rise 
of  temperature  on  compression  than  any  method  involving  a  ther- 
mometer. 

In  the  case  of  mercury  (in  jacket  IV),  contact  was  at  first  broken 
upon  rapid  compression  at  500  kg. /cm*,  with  a  quantity  of  mercury 
which  finally  gave  a  reading  of  366  kg. /cm1,  when  the  heat  of  com- 
pression had  been  taken  away.  Thus  the  pressure  of  500  atmos- 
pheres caused  a  rise  of  temperature  enough  to  cause  an  error  of  134 
atmospheres,  which  corresponds  to  an  increase  in  the  volume  of  the 
mercury  of  0.0040  milliliter,  a  value  taken  from  the  curve  for  this 
jacket  or  easily  calculated  from  the  mercury-glass  curve  given  on  page 
19.' 

There  were  present  21.6  milliliters  of  mercury,  hence  the  per- 
centage expansion  was  0.0185.  But  a  rise  of  i°  would  cause  an  ex- 
pansion of  0.0157  Per  cent-  ^  the  glass  were  warmed  also  to  the  same 
extent,  or  0.0182  if  the  glass  were  stationary  in  temperature.  Hence 
the  rise  of  temperature  on  compressing  the  mercury  to  500  atmospheres 
must  have  been  somewhere  between  1.2°  and  1.0°,  according  to  the 
supposition  adopted  concerning  the  glass.  The  higher  of  these  two 
results  is  the  more  probable,  and  even  this  may  be  too  low  because  of 
the  exceedingly  rapid  loss  of  heat  from  this  system  assumed  to  be  in 
an  adiabatic  condition. 

Another  mode  of  stating  this  calculation  may  make  the  matter 
clearer.  The  coefficients  of  cubic  expansion  and  compressibility  are 
respectively  represented  by  the  ratios  (8v/8t)p  and  (3vjdp)t.  If  now 
we  make  (dv  )f  =  (fa>), —  a  proceeding  actually  carried  out  in  the 
above  experiment —  the  following  equation  is  obtained  by  dividing  one 
by  the  other. 

Sf        coeff.  of  compress. 
Sp  ~    coeff.  of  expans. 

From  this  equation 

St=  *34X  0.0000014^  r  2 
0.000157 

a  result  identical  with  that  obtained  before.  In  this  case,  of  course, 
since  the  actual  change  of  pressure  is  the  value  used  in  the  expression, 

'  The  change  of  compressibility  with  temperature  and  pressure  are  neglected 
in  this  calculation  as  being  infinitesimals  of  the  second  order. 


HEAT    OF    COMPRESSION 


41 


the  actual  coefficients  corresponding  to  the  mercury  and  glass  together 
must  be  used  in  the  calculations. 

The  heat  of  compression  of  a  cubic  centimeter  of  mercury  over  the 
pressure  range  of  500  atmospheres  is  thus  about  13.5  x  1.2  X  0.033 
X  4.2  =  2.3  joules.  This  value  is  probably  too  low  rather  than  too 
high. 

In  the  case  of  water  the  pressure-difference  between  the  adiabatic 
and  isothermal  readings  was  much  smaller,  being  only  9.5  units  of 
pressure  for  a  pressure  range  of  416  units.  Since  in  the  experiment 
with  this  same  jacket  containing  water,  97.5  units  of  pressure  corre- 
sponded with  1.034  grams  of  added  mercury,  the  difference  of  9.5 
units  must  have  signified  an  addition  of  o.io  gram  or  0.0075  mu>h'- 
liter  of  mercury.  The  volume  of  water  was  18.75  milliliters,  hence 
the  percentage  expansion  was  0.040.  But  a  rise  of  temperature  of  i° 
would  cause  a  percentage  expansion  of  about  0.02,  hence  the  rise  of 
temperature  must  have  been  about  2°.  This  signifies  the  evolution  of 
nearly  9  joules  of  heat  under  compression  to  416  units  of  pressure,  or 
about  ii  joules  under  compression  to  500  units  of  pressure.  The 
amount  is  large,  being  nearly  five  times  as  great  as  the  corresponding 
heat  of  compression  of  mercury.  In  this  case,  as  in  the  preceding  one, 
the  cooling  effect  probably  introduces  a  large  error;  the  results  are 
given  as  preliminary  examples  of  an  application  of  the  apparatus, 
rather  than  as  a  precise  evaluation  of  the  effect.  With  greater  precau- 
tions a  more  exact  result  might  be  obtained ;  and  we  hope  to  test  the 
method  further. 

A  HIGH  PRESSURE  MANOMETER  AND  THE  UNIT  OF  PRESSURE. 

The  properties  of  a  few  pure  substances  serve  as  the  most  convenient 
and  generally  useful  means  of  defining  by  comparison  the  properties 
of  all  substances  and  the  various  dimensions  of  energy.  Thus  specific 
gravities  and  specific  heats  usually  serve  as  the  means  of  determining 
densities  and  heat  capacities ;  the  temperature  scale  is  defined  by  the 
triple  or  quadruple  or  other  fixed  points  of  a  few  elements  or  simple 
compounds  and  subdivided  by  the  tension-increase  of  hydrogen  in  con- 
stant volume ;  electromotive  force  is  found  by  comparison  with  a 
Clark  or  Weston  cell ;  electrical  quantity  is  determined  by  the  weight 
of  a  pure  metal  which  it  can  deionize,  and  so  forth.  It  seems  to  us 
desirable  to  define  the  measurement  of  high  pressures  also  in  an 
equally  convenient  way  by  reference  to  the  compressibility  of  one  or 
more  easily  obtained  pure  liquid  substances.  The  problem  is  a  diffi- 
cult one,  because  the  apparatus  used  for  containing  the  material  may 


42  NEW    METHOD    OF    DETERMINING    COMPRESSIBILITY 

be  distorted  by  the  strain  of  compression ;  but  with  the  help  of  our 
glass  jacket  the  result  is  very  easily  attained. 

If  glass  were  a  definite  substance,  the  figures  given  in  the  table  of 
data  concerning  the  compressibility  of  water  alone  or  of  mercury  alone, 
would  at  once  afford  the  desired  intelligence.  By  plotting  the  results 
in  the  second  and  third  column  on  page  38  for  example,  it  is  readily 
seen  that  in  a  glass  jacket  containing  18.75  milliliters  of  water  and  1.9 
milliliters  of  mercury  at  20°,  100  kilograms  per  square  centimeter 
would  correspond  to  1.050  grams  of  added  mercury,  200  units  of 
pressure  would  correspond  to  2.086  grams  of  added  mercury  and  so 
forth.  The  same  proportion  of  change  of  volume  to  total  volumes  of 
water  and  mercury  would  exist  in  a  jacket  of  any  other  size.  Unfor- 
tunately, however,  the  compressibility  of  glass  is  not  uniform  enough 
in  different  samples  to  make  such  an  inference  more  definite  than 
within  three  tenths  of  one  per  cent. 

On  the  other  hand,  the  difference  between  the  compression  of  water 
and  mercury,  as  found  by  a  jacket  of  this  kind,  is  perfectly  definite 
and  free  from  all  uncertainty  connected  with  the  glass.  This  difference 
is  plotted  as  the  curve  for  water,  on  the  larger  diagram  (Fig.  5),  and 
will  serve  at  any  time  as  a  means  of  comparing  any  other  gauge  with 
that  made  by  Schaeffer  and  Budenberg,  thus  enabling  any  one  who  has 
a  less  accurate  gauge  to  correct  its  readings,  or  any  one  who  has  a  more 
accurate  guage  to  correct  ours. 

The  best  method  of  making  this  comparison  would  be  to  make  suc- 
cessive series  of  experiments  first  with  mercury  and  afterwards  with 
water  in  a  given  glass  jacket,  in  the  way  described  above,  and  then  to 
plot  the  results  and  compare  the  differences  with  ours.  The  curves  are 
so  nearly  straight  lines  that  they  may  be  drawn  with  great  accuracy  by 
bending  a  thin  ruler  made  of  wood  with  an  even  grain,  until  all  the 
points  are  covered. 

From  our  preliminary  experiments  it  seems  probable  that  the  sen- 
sitiveness of  this  manometer  is  very  great.  Under  favorable  condi- 
tions the  method  is  able  to  detect  ^  atmosphere  in  i  ,000  atmospheres 
or  one  part  in  20,000. 

It  is  our  purpose  to  carry  out  the  evaluation  of  this  manometric 
method  with  much  greater  precision  than  has  been  heretofore  possible, 
in  an  apparatus  free  from  ground  glass  joints.  The  present  results  in 
this  direction  must  be  considered  as  merely  preliminary,  but  even  these 
may  serve  an  end  hitherto  unattainable. 

It  is  a  matter  of  great  regret  that  the  scientific  world  has  not  agreed 
upon  a  less  arbitrary  unit  of  pressure  than  the  ' '  atmosphere."  The  diffi- 


UNIT    OF    PRESSURE 


43 


culty  is  now  increased  by  the  frequent  technical  use  of  this  word  to 
designate  the  pressure  of  a  kilogram  per  square  centimeter.  The 
growing  tendency  toward  the  adoption  of  the  c.g.s.  system  suggests 
the  use  of  a  consistent  unit  for  this  dimension  also.  Might  not  the 
pressure  of  a  dyne  per  square  centimeter  be  suitably  called  a  bar? 
(Greek  /5a/;«^,  pressure,  weight.)  This  suggestion  is  made  because  the 
practical  use  of  a  unit  is  always  much  facilitated  by  a  definite  verbal 
designation.  In  this  case,  the  pressure  of  a  megadyne  per  square  cen- 
timeter would  be  called  a  megabar,  a  name  no  more  cumbrous  than 
atmosphere,  and  far  more  definite.  This  unit,  though  unnamed,  has 
long  been  advocated  by  Ostwald  as  a  more  scientific  one  than  the 
present  standard.1  The  megabar  is  1,000/980.6  =  101.98  per  cent,  of 
a  kilogram  per  square  centimeter,  or  101.98/1,033.2  =  98.703  per  cent, 
of  an  atmosphere,  or  the  pressure  measured  by  75.015  centimeters  of 
mercury  at  o°  C.,  at  sea  level,  and  45°  of  latitude.  This  pressure  is 
more  nearly  the  average  atmospheric  pressure  at  the  laboratories  of  the 
world  than  the  arbitrary  atmosphere  usually  taken.  A  megabar,  act- 
ing through  the  volume  of  a  cubic  centimeter  or  milliliter,  performs  a 
megerg  of  work,  or  one-tenth  of  a  joule.  For  the  convenience  of  pos- 
sible users  of  the  new  results,  all  are  tabulated  below  on  the  basis  of 
each  one  of  these  three  standards  of  pressure. 

TABLE  OF  COMPRESSIBILITIES  AT  20°  C. 

The  values  given  below  are  multiplied  by  io6  in  order  to  economize  space. 
Brackets  signify  partial  extrapolation. 


Range 
of  Pressure. 

I» 

Br, 

ci, 

ecu 

CHCl, 

CHBr3 

H20 

p4 

Hg 

3-80 

3-75 
3-72 
3-69 
3-64 

kgs.  per  cm2. 
0-100 
100-200 
200-300 
300-400 
400-500 

[13] 
13 
12 

[61.3] 
56.3 
52.7 
50.2 
48.1 

112' 
I'io7" 
-98; 
87 

l!  8l. 

[90.0] 

82.0 
74-2 
68.6 

[ia] 

77.2 
70.2 
65.3 

[49-1] 
45-8 
42.5 
4°-5 
[39-5] 

[44-3] 

43-3 
41.0 
40.3 
38.6 

[20.9] 
20.4 
19.9 
19.8 
19.6 

megabars. 

O-IOO 
100-200 
200-300 
300-400 
4OO-5OO 

[13] 
13 
13 

[62.5] 

57-4 
53-7 
51.2 
49.0 

'114' 
;ios; 

'100' 

FS 

[£? 

83.6 
75-7 
69.9 

[93.2] 

88.1 
78.7 
71.6 
66.6 

[50.1] 
46.7 
43-3 
4i.3_ 
[40.3] 

[45.2] 
44-1 
41.8 
41.1 
39-4 

[21-3] 

20.8 

20.3 

20.2 
20.0 

IS 

19 

3.71 

atmospheres. 
O-IOO 
100-200 
200-300 
300-400 
400-500 

[14] 
13 
13 

[56if 

54-5 
51-9 
49-7 

;«$ 
lii°. 
'102" 

[5: 

[93-1] 
89.6 

84.7 
76.7 
70.9 

[94.5] 
89.4 
79-8 
72.6 
67.6 

[50.8] 
47-4 
43-9 
41.1 
[40-8] 

[45-8] 
[44-8] 
42.4 
41-7 
39-9 

[21.6] 
21.  1 
20.6 
20.4 
20.2 

3.92 
3.87 
3.84 
3.81 
3.76 

^rundriss  allgem.  Chem.,  p.  54  (1899). 


44  NEW    METHOD    FOR    DETERMINING    COMPRESSIBILITY 

CHANGE  OF  COMPRESSIBILITY  WITH  PRESSURE. 

A  glance  at  the  above  table  shows  that  all  the  substances  studied, 
like  all  those  examined  by  Barus,  show  a  decrease  in  compressibility 
with  increasing,  pressure.  This  decrease  is  by  no  means  a  simple 
function,  however.  Leaving  out  of  consideration  the  cases  of  chlorine 
and  iodine,  which  cannot  claim  accuracy  enough  for  serious  considera- 
tion in  a  discussion  of  this  kind,  the  other  substances  show  the  follow- 
ing percentage  decrease  in  their  compressibilities  between  100  and  500 
atmospheres:  CHC1,  29,  CC14,  26;  Br,  21;  CHBrs,  20.6;  H,O, 
13 ;  Hg,  4.  This  order  is  arranged  according  to  the  magnitude  of 
the  compressibility,  and  it  exhibits  a  steady  decrease ;  hence  one  may 
infer  that,  other  things  being  equal,  the  greater  the  compressibility,  the 
greater  is  its  percentage  decrease  with  increasing  pressure.  That  other 
circumstances  influence  this  relation  is  shown  however  by  the  fact  that 
chloroform  and  carbon  tetrachloride  manifest  different  second  differen- 
tial quotients  although  their  first  differential  quotients  are  exactly  iden- 
tical at  150  atmospheres.  Moreover,  bromoform  and  water  have 
almost  the  same  compressibility,  and  yet  the  change  of  this  compres- 
sibility with  the  pressure  is  noticeably  different.  Such  differences  as 
this  must  be  referred  to  the  specific  natures  of  the  component  ele- 
ments, and  the  internal  pressure  relations  within  each  substance. 

When  the  theorizer  goes  further  than  such  a  comparison  as  this,  and 
attempts  to  determine  the  mathematical  expressions  for  these  curves, 
he  is  met  by  a  serious  obstacle.  The  departure  from  the  perfectly 
linear  equation  x  =  ay  is  not  sufficiently  greater  than  the  possible  error 
of  the  gauge  to  make  its  somewhat  subtle  nature  clearly  manifest. 
One  should  point  out  also  the  probability  that  the  parabolic  equations 
proposed  by  Barus  for  the  organic  liquids  studied  by  him  are  subject 
to  an  even  greater  experimental  uncertainty ;  so  that  it  is  safe  to  say 
that  no  data  now  known  to  us  afford  a  satisfactory  basis  for  the  deter- 
mination of  the  law  underlying  the  change  of  compressibility  with 
pressure.  It  is  our  hope,  by  more  accurate  experiments  made  upon 
larger  quantities  of  material  and  with  a  more  perfect  gauge,  to  pro- 
ceed further  in  this  direction. 

In  conclusion,  it  is  a  pleasure  to  express  our  great  indebtedness  to 
the  Cyrus  M.  Warren  Fund  of  Harvard  University  for  assistance  in 
the  early  part  of  this  investigation,  and  to  the  Carnegie  Institution  of 
Washington  for  assistance  in  the  latter  part. 


45 


SUMMARY. 


In  this   paper  the  following  additions  to  the  knowledge  of  com- 
pressibility are  made  : 

1 .  The  practical  errors  of  many  previously  used  methods  have  been 
demonstrated. 

2.  New  methods  have  been  suggested  which  are  applicable  to  nearly 
all  solids  and  liquids. 

3.  With  the  help  of  these  methods,  the  compressibility  of  bromine, 
iodine,    chloroform,    bromoform,    carbon   tetrachloride,    phosphorus, 
water  and  glass  have  been  determined  by  reference  to  mercury,  in 
most  cases  as  far  as  500  or  600  atmospheres.     These  are  recorded  on 

P-  43- 

4.  From  some  of  these  the  compressibility  of  liquid  chlorine  has 
been  inferred. 

5 .  Approximate  determinations  of  the  heats  of  compression  of  water 
and  mercury  have  been  made. 

6.  A  new  manometer  for  calibrating  high  pressure  gauges  is  pro- 
posed. 

7.  The  word  mcgabar  is  suggested  as  a  convenient  name  for  the 
pressure  of  a  megadyne  on  a  square  centimeter,  and  the  use  of  this 
absolute  standard  is  urged. 

8.  The  compressibilities  of  the  substances  named  above  have  been 
compared  with  regard  to  their  relative  decrease  with  increasing  pressure. 
It  is  pointed  out  that  usually  the  greater  the  compressibility  the  greater 
is  its  decrease  with  increasing  pressure. 


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